Last updated on May 14th, 2018

Excel has many features which can perform different tasks. Beside performing different statistical, financial analysis we can solve equations in Excel. In this article, we will analyze a popular topic which is Solving Equations in Excel.

In this article, we will solve different kinds of equations like cubic, polynomial, linear, quadratic with different features of Excel.

Table of Contents

- 1 Solving Polynomial Equations in Excel
- 2 Solve Cubic Equation in Excel using Goal Seek
- 3 Solve Cubic Equation in Excel using Solver
- 4 Solve Quadratic Equation in Excel using Goal Seek Feature
- 5 Use of Solver to Solve Quadratic Equation in Excel
- 6 Solve Quadratic Equation in Excel using Formula
- 7 Solve Linear Equations in Excel with Matrix System
- 8 Solving Linear Equations in Excel Using Solver
- 9 Download Working File
- 10 Conclusion

## Solving Polynomial Equations in Excel

A polynomial equation/function can be quadratic, linear, quartic, cubic and so on. The Polynomial equations don’t contain a negative power of its variables. Different kind of polynomial equations example is given below.

1) Monomial: y=mx+c

2) Binomial: y=ax^{2}+bx+c

3) Trinomial: y=ax^{3}+bx^{2}+cx+d

With the direct calculation method, we will also discuss other methods like Goal Seek, Array, and Solver in this article to solve different polynomial equations.

**Read More: ****3D Referencing & External Reference in Excel**

## Solve Cubic Equation in Excel using Goal Seek

Let`s say we have a cubic equation which is **Y=5x ^{3}-2x^{2}+3x-6**. We will solve this equation for finding the value of “X” with a specific value of “Y”. We will use the Excel

**Goal Seek**feature here to solve the equation. The procedure is given below.

- First set the coefficients in different cells.
- Set the initial value of X as “0” in cell B6.
- After that write the polynomial equation in cell G3 with respect to the cells of coefficients and the initial value of X.

- Now, under the
**Data**tab click on to the**Goal Seek**option under the**Forecast**option.

- In the
**Goal Seek**dialogue box, insert the inputs as follows and press on**OK**.

- The Goal Seek feature will do some iterations for the final value of Y which is set as 15 in this example.

- After the Goal Seek completes its operation you will see the initial value of X and the cell where the formula was placed is changed. Now the initial value is showing the value of X when the value of Y becomes 15.

## Solve Cubic Equation in Excel using Solver

You can also use the Solver feature of Excel to solve cubic equations. Let`s solve the previous equation for a better understanding.

- Just after typing the equation in cell G3, click on to solver which is under Analysis option of Data tab.
- In the
**Solver Parameters**dialogue box, do the following and press the**Solve**option.

- Here we set the target value 15. B6 is the variable cell here. As it is a non-linear equation the solving method was selected as
**GRG Nonlinear**. - The below result will be found after the operation.

**Read More: ****How to use Goal Seek to find an input value**

## Solve Quadratic Equation in Excel using Goal Seek Feature

Let`s solve a quadratic equation which is Y=3x^{2}+6x-5. We will see how this equation can be solved with the Goal Seek feature. The procedures are given below.

- First set the coefficients in different cells.
- Set the initial value of X as “0” in cell B6.
- After that write the equation in cell F3 with respect to the cells of coefficients and the initial value of X.

- Now, under the
**Data**tab click on to the**Goal Seek**option under the**Forecast**option.

- In the Goal Seek dialogue box, insert the inputs as follows and press on
**OK**.

- The
**Goal Seek**feature will do some irritations for the final value of Y which is set as 12 in this example.

- After the Goal Seek completes its operation you will see the initial value of X and the cell where the formula was placed is changed. Now the initial value is showing the value of X when the value of Y becomes 12.

**Read More: ****Data Analysis in Excel – Learn 10 Common Statistical Terms**

## Use of Solver to Solve Quadratic Equation in Excel

You can also use the Solver feature of Excel to solve quadratic equations. Let`s solve the same equation for a better understanding.

- Just after typing the equation in cell F3, click on to solver which is under Analysis option of Data tab.
- In the
**Solver parameters**dialogue box, do the following and press**Solve**.

- Here we set the target value 15. B6 is the variable cell here. As it is a non-linear equation the solving method was selected as
**GRG Nonlinear**. - The below result will be found after the operation.

## Solve Quadratic Equation in Excel using Formula

The format of a quadratic equation is **x=(-b±√(b^2-4ac))/2a** **.**By using this formula directly we can find the roots of the quadratic function. In the below picture we calculate the roots of the quadratic functions. Here the roots are X1 and X2.

## Solve Linear Equations in Excel with Matrix System

We can use matrix system to solve a set of linear equations in excel. Let`s say we have 3 equations where the values of x, y, and z are unknown. The equations are,

3x+2y+z=8……………… (1)

11x-9y+23=27…………..(2)

8x-5y=10….………………(3)

We will use the formula X=A^{-1}B. Where both A^{-1} and B are the arrays. The procedure of solving the set of linear equations is given below.

- Write down the coefficients of x, y, and z along with constants in an array form just like the picture below. The coefficients of x, y and z are set of matrix A and the constants are set of matrix B.

- Now select the range
**B11:D13**and write down the formula =**MINVERSE(B7:D9)**and press Ctrl+Shift+Enter together to use this formula as an array.

- Now to find the result of
**X**select the range**G11:G13**and enter the formula**=MMULT(B11:D13,G7:G9)**and press Ctrl+Shift+Enter together to use this formula as an array. This function returns the matrix product of the two arrays. Here B11:D13 is the array set of A^{-1}and G7:G9 is the array set of

## Solving Linear Equations in Excel Using Solver

It`s quite easy to find the variables of different linear equations using solver. The procedure is shown below.

- Make a table named
**Value of Variables**in your worksheet and keep some blank spaces beside x, y, and z. - Make another table which contains the equations with variables and the constants.
- In the Equations column (Column E) write down the equations, =3*C7+2*C8+C9, =11*C7-9*C8+23*C9 and =8*C7-5*C8. We use the formula
**=FORMULATEXT()**to show these equations in column F. The constants are written in column G.

- Click on to
**Solver**which is under**Analysis**option of**Data** - In Solver Parameters dialogue box, set the
**Set Objectives**as $E$7, select the**Value of**option and type 8. In the**by changing variable cells option**write $C$7:$C$9**. Uncheck the Make Unconstrained Variables Non-Negative**and select Simplex LP in the**Select a Solving Method Option.**

- Press on to
**Add**in the**Solve Parameters**dialogue box. - In the
**Add Constraint**, dialogue box, do the followings and press on to**Add.**

- It`s time to gather the information of last equation as the input of solver. Do the followings and press
**OK**.

- After this, your
**Solver Parameters**will look like the picture below. Press on to the Solve option to continue the operation.

- After you press on to the
**Solve**option you will see the change in the**Values of the Variables**The values that you get in this table are the actual values of the variables x, y, and z.

**Note:**After you press on to the Solve option you will get a new dialogue box of

**Solver Results**. Press on to the

**Keep Solver Solution**and click

**OK**to make the changes in your worksheet.

**Related: How to solve simultaneous linear equations in Excel using Solver**

## Download Working File

## Conclusion

In this article, we see various processes of solving many different kinds of equations. Out of the many processes, the **Solver** in Excel is the best option. In Solver you can not only find the roots of the equation, you can also find the values of different variables simultaneously. The Solver in Excel makes it easy for the users to perform the linear programming problems.

Hope this article meets your expectations. Looking forward to your feedback.

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.

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