# How to Solve a Polynomial Equation in Excel -5 Simple Methods

Polynomial equations up to the third order will be used here, although these methods can also be applied to higher-order polynomials.

### Method 1 – Using the Goal Seek Option

If you know the result of a polynomial, you can use the Goal Seek feature to find the input that produces that result.

Steps:

• Double-click on B7 and enter the following formula:
`=(5*C7^3)-(2*C7^2)+(3*C7)-6`
• Then, enter a value for X in C5.

• Go to the Data tab and choose Forecast.
• In What-If Analysis, click Goal seek.

• Enter the values as in the image below and click OK.

### Method 2 – Utilizing the Solver Feature

The Solver tool in Excel uses operations research methods to find the optimal solution from a set of equations.

Steps:

• Open the Solver tool in the Data tab.

• Enter the following parameters in Solver Parameters.

• Click Solve and the Solver will calculate the value of X.

### Method 3-Â  Solving a Quadratic Polynomials Equation

Steps:

• Click C9 and enter the formula:
`=(-C7+SQRT(C7^2-4*C6*C8))/(2*C6)`

• Enter this formula in C10:
`=(-C7-SQRT(C7^2-4*C6*C8))/(2*C6)`

• Press Enter to see the solutions of X.

### Method 4 – Finding the Solution of a Multivariable Equation by using the MINVERSE Function

The MINVERSE function in Excel returns the inverse of a given array, but it can be used to solve a multivariable polynomial equation.

3x+2y+z=8

11x+-9y+23=27

8x-5y=10

Steps:

• Select the range B10:D12 and enter the following formula:
`=MINVERSE(B5:D7)`
• Press Ctrl+Shift+Enter and you will see the inverse values.

• Select the range F10:F12 and enter the following formula:
`=MMULT(B10:D12,E5:E7)`
• Press Ctrl+Shift+Enter and you will see the values of x, y, and z.

### Method 5 – Using the Solver to Find the Solution of a Multivariable Equation

The 3 equations from the previous method will be used.

Steps:

• Double-click E5 and enter the formula below:
`=3*C5+2*C6+C7`
• Copy this formula to the cells below using the Fill Handle.

• Click F5 and enter this formula:
`=FORMULATEXT(E5)`
• Copy this formula to the cells below.

• Open the Solver and enter the parameters.

• Note that you need to click Add after entering each constraint.

• ClickÂ  Solve option to see the solutions.

## Related Articles

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Nazmul Hossain Shovon

Nazmul Hossain Shovon, a BUET graduate in Naval Architecture and Marine Engineering, embarked on his career with 8 months dedicated to the Exceldemy project's triumph. Transitioning into a Software Developer role, he specialized in web add-in development. At Exceldemy, he authored about 125 blog articles and solved many visitorsâ€™ problems, refining his writing skills and delving into Excel-related topics. With a primary passion for programming and software development, Shovon continually explores new horizons, fostering professional growth in his... Read Full Bio

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