Excel has many features that can perform different tasks. Besides performing different statistical, and financial analyses, we can solve equations in Excel. In this article, we will analyze a popular topic which is Solving Equations in Excel in different ways with proper illustrations.

**Solving Equations in Excel: 5 Examples**

Before starting to solve equations in Excel, let’s see which kind of equation will be solved with which methods.

**Types of Solvable Equations in Excel:**

There are different kinds of equations exist. But all are not possible to solve in Excel. In this article, we will solve the following types of equations.

**Cubic equation,****Quadratic equation,****Linear equation,****Exponential equation,****Differential equation,****Non-linear equation**

**Excel Tools to Solve Equations: **

There are some dedicated tools to solve equations in Excel like **Excel Solver** Add-in and **Goal Seek** Feature. Besides, you can solve equations in Excel numerically/manually, using Matrix System, etc.

### 1. Solving Polynomial Equations in Excel

**polynomial**equation is a combination of variables and coefficients with arithmetic operations.

In this section, we will try to solve different polynomial equations like cubic, quadrature, linear, etc.

#### 1.1 Solving Cubic Equation

**polynomial**equation with degree three is called a

**cubic**polynomial equation.

Here, we will show two ways to solve a cubic equation in Excel.

##### i. Using Goal Seek

Here, we will use the Goal Seek feature of Excel to solve this cubic equation.

Assume, we have an equation:

**Y= 5X**

^{3}-2X^{2}+3X-6We have to solve this equation and find the value of **X**.

**📌 ****Steps:**

- First, we separate the coefficients into four cells.

- We want to find out the value of
**X**here. Assume the initial value of**X**is**zero**and insert**zero (0)**on the corresponding cell.

- Now, formulate the given equation of the corresponding cell of
**Y**. - Then, press the
**Enter**button and get the value of**Y**.

`=C5*C7^3+D5*C7^2+E5*C7+F5`

- Then, press the
**Enter**button and get the value of**Y**.

Now, we will introduce the **Goal Seek** feature.

- Click on the
**Data**tab. - Choose the
**Goal Seek**option from the**What-If-Analysis**section.

- The
**Goal Seek**dialog box appears.

We have to insert cell reference and value here.

- Choose
**Cell H5**as the**Set cell.**This cell contains the equation. - Select
**Cell C7**as the**By changing cell**, which is the variable. The value of this variable will change after the operation.

- Put
**20**on the**To value**box, which is a value assumed for the equation.

- Finally, press the
**OK**button.

The status of the operation is showing. Depending on our given target value, this operation calculated the value of the variable on **Cell C7**.

- Again, press
**OK**there.

It is the final value of **X**.

##### ii. Using Solver Add-In

**Solver **is an **Add-in**. In this section, we will use this **Solver **add-in to solve the given equation and get the value of the variable.

**Solver **add-ins do not exist in Excel default. We have to add this add-in first.

**📌 ****Steps:**

- We set the value of the variable
**zero (0)**in the dataset.

- Go to
**File**>>**Options**. - The
**Excel Options**window appears. - Choose
**Add-ins**from the left side. - Select
**Excel Add-ins**and click on the**Go**button.

- The
**Add-ins**window appears. - Check the
**Solver Add-in**option and click on**OK**.

- We can see the
**Solver**add-in in the**Data**tab. - Click on the
**Solver**.

- The
**Solver Parameters**window appears.

- We insert the cell reference of the equation on the
**Set Object**box. - Then, check the
**Value of**the option and put**20**on the corresponding box. - Insert the cell reference of the variable box.
- Finally, click on
**Solver**.

- Choose
**Keep Solver Solution**and then press**OK**.

- Look at the dataset.

We can see the value of the variable has been changed.

#### 1.2 Solving Quadratic Equation

**quadratic**

**polynomial**equation.

Here, we will show two ways to solve a quadratic equation in Excel.

We will solve the following quadratic equation here.

**Y=3X**

^{2}+6X-5##### i. Solve Using Goal Seek Feature

We will solve this quadratic equation using the **Goal Seek** feature. Have a look at the below section.

**📌 ****Steps:**

- First, we separate the coefficients of the variables.

- Set the initial value of
**X**zero (0). - Also, insert the given equation using the cell references on
**Cell G5**.

`=C5*C7^2+D5*C7+E5`

- Press the
**Enter**button now.

We get a value of **Y** considering **X** is zero.

Now, we will use the **Goal Seek** feature to get the value of **X**. We already showed how to enable the **Goal Seek** feature.

- Put the cell reference of the variable and equation on the
**Goal Seek**dialog box - Assume the value of equation
**18**and put it in the box of the**To value**section.

- Finally, press
**OK**.

We get the final value of variable **X**.

##### ii. Using Solver Add-In

We already showed how to add **Solver Add-in** in Excel. In this section, we will use this **Solver **to solve the following equation.

**📌 ****Steps:**

- We put
**zero**(**0**) on**Cell C7**as the initial value of**X**. - Then, put the following formula on
**Cell G5**.

- Press the
**Enter**button.

- Enter the
**Solver**add-in as shown before. - Choose the cell reference of the equation as the object.
- Put the cell reference of the variable.
- Also, set the value of the equation as
**18**. - Finally, click on the
**Solve**option.

- Check the
**Keep Solver Solution**option from the**Solver Results**window.

- Finally, click the
**OK**button.

### 2. Solving Linear Equations

An equation that has any variable with a maximum degree of **1** is called a linear equation.

#### 2.1 Using Matrix System

**The MINVERSE function** returns the inverse matrix for the matrix stored in an array.

**The MMULT function** returns the matrix product of two arrays, an array with the same number of rows as **array1** and columns as **array2**.

This method will use a matrix system to solve linear equations. Here, **3** linear equations are given with **3** variables **x**, **y**, and **z**. The equations are:

**3x+2+y+z=8,**

**11x-9y+23z=27,**

**8x-5y=10**

We will use the **MINVERSE** and **MMULT** functions to solve the given equations.

**📌 ****Steps:**

- First, we will separate the coefficients variable in the different cells and format them as a matrix.
- We made two matrices. One with the coefficients of the variable and another one of the constants.

- We add another two matrices for our calculation.

- Then, we will find out the inverse matrix of
**A**using the**MINVERSE**function. - Insert the following formula on
**Cell C7**.

`=MINVERSE(C5:E7)`

This is an array formula.

- Press the
**Enter**button.

The inverse matrix has formed successfully.

- Now, we will apply a formula based on the
**MMULT**function on**Cell H9**.

`=MMULT(C9:E11,H5:H7)`

We used two matrices of size **3**x**3** and **3**x**1** in the formula and the resultant matrix is of size **3**x**1**.

- Press the
**Enter**button again.

This is the solution of the variables used in the linear equations.

#### 2.2 Using Solver Add-In

We will use the Excel Solver for linear programming to solve **3** equations with **3** variables.

**📌 ****Steps:**

- First, we separate the coefficients as shown previously.

- Then, add two sections for the values of the variables and insert the equations.
- We set the initial value of the variables to
**zero**(**0**).

- Insert the following three equations on cells
**E10**to**E12**.

`=C5*C10+D5*C11+E5*C12`

`=C6*C10+D6*C11+E6*C12`

`=C7*C10+D7*C11+E7*C12`

- Now, go to the
**Solver**feature. - Set the cell reference of the 1st equation as the objective.
- Set the value of equation
**8**. - Insert the range of the variables in the marked box.
- Then, click the
**Add**button.

- The
**Add Constraint**window appears. - Put the cell Reference and values as marked in the below image.

- Insert the second constraint.
- Finally, press
**OK**.

- Constraints are added. Press the
**Solve**button.

- Look at the dataset.

We can see the value of the variables has been changed.

#### 2.3 Using Cramer’s Rule for Solving Simultaneous Equations with 3 Variables in Excel

When two or more linear equations have the same variables and can be solved at the same time are called simultaneous equations. We will solve the simultaneous equations using **Cramer’s **rule. The function **MDETERM** will be used to find out the determinants.

**MDETERM**function returns the matrix determinant of an array.

**📌 ****Steps:**

- Separate the coefficients into
**LHS**and**RHS**.

- We add
**4**sections to construct a matrix using the existing data.

- We will use the data of
**LHS**to construct**Matrix D**.

- Now, we will construct
**Matrix Dx.** - Just replace the coefficients of
**X**with the**RHS**.

- Similarly, construct
**Dy**and**Dz**matrices.

- Put the following formula on
**Cell F11**to get the determinant of**Matrix D**.

`=MDETERM(C10:E12)`

- Press the
**Enter**button.

- Similarly, find the determinants of Dx, Dy, and Dz by applying the following formulas.

**)**

`=MDETERM(C14:E16`

`=MDETERM(C18:E20)`

`=MDETERM(C22:E24)`

- Move to
**Cell I6**. - Divide the determinant of
**Dx**by**D**to calculate the value of**X**.

`=F15/F11`

- Press the
**Enter**button to get the result.

- In the same way, get the value of
**Y**and**Z**using the following formulas:

`=F19/F11`

`=F23/F11`

Finally, we solve the simultaneous equations and get the value of the three variables.

### 3. Solving Nonlinear Equations in Excel

**2**or more than

**2**and that does not form a straight line is called a

**non-linear equation.**

In this method, we will solve non-linear equations in Excel using the **Solver **feature of Excel.

We have two non-linear equations here.

**📌 ****Steps:**

- We insert the equation and variables into the dataset.

- First, we consider the value of the variable
**zero**(**0**) and insert that into the dataset.

- Now, insert two equations on
**Cell C5**and**C6**to get the value of the**RHS**.

`=C9^2+C10^2-25`

`=C9-C10^2`

- We add a new row in the dataset for sum.
- After that, put the following equation on
**Cell C12**.

`=SUM(C5:C6)`

- Press the
**Enter**button and the sum of the**RHS**of both equations.

- Here, we will apply the
**Solver**feature of Excel. - Insert the cell references on the marked boxes.
- Set the
**Value of 0.** - Then, click on the
**Add**button to add constraints.

- We add the
**1st**constraints as shown in the image. - Again, press the
**Add**button for**2nd**constraint.

- Input the cell references and values.
- Finally, press
**OK**.

- We can see constraints are added in the
**Solver**. - Click the
**Solver**button.

- Check the
**Keep Solver Solution**option and then click on**OK**.

- Look at the dataset now.

We get the value of **X **and **Y **successfully.

### 4. Solving an Exponential Equation

**exponential equation**is with variable and constant. In the exponential equation, the variable is considered as the power or degree of the base or constant.

In this method, we will show how to solve an exponential equation using the **EXP **function.

**The EXP function**returns e raised to the power of a given number.

We will calculate the future population of an area with a target growth rate. We will follow the below equation for this.

Here,

** Po**= Current or initial population

** R**= Growth rate

** T**= Time

* P*= Esteemed for the future population.

This equation has an exponential part, for which we will use the **EXP **function.

**📌 ****Steps:**

- Here, the current population, target growth rate, and the number of years are given in the dataset. We will calculate the future population using those values.

- Put the following formula based on the
**EXP**function on**Cell C7**.

`=ROUND(C4*EXP(C5*C6),0)`

We used the **ROUND **function, as the population must be an integer.

- Now, press the
**Enter**button to get the result.

It is the future population after **10 **years as per the assumed growth rate.

### 5. Solving Differential Equations in Excel

**differential**equation. The derivative may be ordinary or partial.

Here, we will show how to solve a differential equation in Excel. We have to find out **dy/dt**, differentiation of **y** concerning **t**. We noted all the information in the dataset.

**📌 ****Steps:**

- Set the initial value of
**n**,**t**, and**y**from the given information.

- Put the following formula on
**Cell C6**for**t**.

`=C5+$G$5`

This formula has been generated from **t(n-1)**.

- Now, press the
**Enter**button.

- Put another formula on
**Cell D6**for**y**.

`=D5+(C5-D5)*$G$5`

This formula has been generated from the equation of **y(n+1)**.

- Again, press the
**Enter**button.

- Now, extend the values to the maximum value of
**t**, which is**1.2**.

We want to draw a graph using the values of **t** and **y**.

- Go to the
**Insert**tab. - Choose a graph from the
**Chart**group.

- Look at the graph.

It is a **y** vs. **t** graph.

- Now, double-click on the graph and the minimum and maximum values of the graph axis. Resize the horizontal line.

- After that, resize the vertical line.

- After customizing the axis, our graph looks like this.

Now, we will find out the differential equation.

- Calculate the differential equation manually and put it on the dataset.

- After that, make an equation based on this equation and put that on
**Cell E5**.

`=-1+C5+1.5*EXP(-C5)`

- Press the
**Enter**button and drag the**Fill Handle**icon.

- Again, go to the graph and press the right button on the mouse.
- Choose the
**Select Data**option from the**Context menu**.

- Select the
**Add**option from the**Select Data Source**window.

- Choose the cells of the
**t**column on**X**values and cells of the**y_exact**column on**Y**values in the**Edit Series**window.

- Again, look at the graph.

**Download Practice Workbook**

Download this practice workbook to exercise while you are reading this article.

**Conclusion**

In this article, we described how to solve different types of equations. I hope this will satisfy your needs in solving several equations in Excel.

why have stooped “Download Article in PDF Format option”

Thanks for asking. It was creating more indexed pages in Google that was bad for us. What you can do is: just you can copy the whole article and paste into a word document and then convert it into a PDF file. There is little chance of getting back of that button.

Best regards

I have a few points that when graphed LOOK like a quadratic equation. How do I go from the set of points to get EXCEL to deliver an EQUATION for the quadratic function given those points (like it can do for LINEAR equations)?

Hello SHAWN S FAHRER!

You can get a quadratic equation from a graph with a few points that you have mentioned here. Follow the steps below for this

First, create a graph with the points you have.

Then, Go to the Chart Elements clicking the Plus icon.

Click on the arrow beside the “Trendline” option.

Go to the “More Options”

1

Here, you will go to a window named “Format Trendline”.

Select the “Polynomial” option of order 2.

Mark the checkbox saying “Display Equation on Chart”.

As a result, you will there will create a trend line following a quadratic equation which is also shown in the graph.

Try this method and let us know the outcome! Thank You!

Hi thanks for posting this article. Can you please elaborate on why did you assume 15 as the value of Y? By definition, shouldn’t we be solving for 3 values of x as the equation is cubic?

Hello MANUJ! You have to insert a value as the set value for cell G3 to use Goal Seek feature.. suppose you have an equation like 5x^3 – 2x^2 + 3x – 21 = 0 then you can change the equation like 5x^3 – 2x^2 + 3x – 6 = 15. Here, we have done this.

And, yes! you are right that the cubic function gives 3 root values. But using the Goal Seek Feature, you will get only one root. and, in many times, the cubic function may have one real root and 2 complex roots. In these cases, the goal seek feature will give the value of the real root.

Try these examples and let us know the output. Thank You!