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- Quadratic Equation

A quadratic equation is of the form ax 2 + bx + c = 0 where a ≠ 0. A quadratic equation can be solved by using the quadratic formula. You can also use Excel's Goal Seek feature to solve a quadratic equation.

1. For example, we have the formula y = 3x 2 - 12x + 9.5. It's easy to calculate y for any given x. For x = 1, y = 0.5

2. For x = 2, y = -2.5

3. But what if we want to know x for any given y? For example, y = 24.5. We need to solve 3x 2 - 12x + 9.5 = 24.5. We can solve the quadratic equation 3x 2 - 12x + 9.5 - 24.5 = 0 by using the quadratic formula.

4. You can use Excel's Goal Seek feature to obtain the exact same result. On the Data tab, in the Forecast group, click What-If Analysis.

5. Click Goal Seek.

The Goal Seek dialog box appears.

6. Select cell B2.

7. Click in the 'To value' box and type 24.5

8. Click in the 'By changing cell' box and select cell A2.

9. Click OK.

Note: Excel returns the solution x = 5. Excel finds the other solution if you start with an x-value closer to x = -1. For example, enter the value 0 into cell A2 and repeat steps 5 to 9. To find the roots, set y = 0 and solve the quadratic equation 3x 2 - 12x + 9.5 = 0. In this case, set 'To value' to 0.

- What-If Analysis

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## How to Solve a Quadratic Equation in Excel (Step-by-Step)

A quadratic equation takes the following form:

Often you will be given the value for y and will be asked to solve for the value of x .

For example, suppose we have the following quadratic equation:

It turns out that setting x = 3 or x = 2 will solve this equation.

To solve quadratic equations in Excel, you can use the Goal Seek function.

The following step-by-step example shows how to use the Goal Seek function in practice.

## Step 1: Enter the Equation

First, let’s enter some random value for x and the formula for the quadratic equation for y:

## Step 2: Find the First X Value Using Goal Seek

Goal Seek finds that the value x=2 (assuming 1.9999 rounds to 2) solves the quadratic equation.

## Step 3: Find the Second X Value Using Goal Seek

For example, we could choose to set the initial x-value to 4:

We can then run the Goal Seek function again and see that it finds a new solution of x=3 :

Thus, the two x-values that can solve this quadratic equation are x=2 and x=3 .

## Additional Resources

The following tutorials explain how to perform other common tasks in Excel:

How to Solve a System of Equations in Excel How to Plot an Equation in Excel

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## How To Solve a Quadratic Equation

## Generic Formula

There are two possible solutions for any quadratic equation. This is one possible solution.

This is the other possible solution.

- A – This is the coefficient of the squared term in the quadratic equation.
- B – This is the coefficient of the single powered term in the quadratic equation.
- C – This is the constant in the quadratic equation.

## What It Does

These formulas will give the solutions to a quadratic equation of the form Ax^2 + Bx + C = 0 .

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## How to solve quadratic equations in Excel - Goal Seek

by Ilker | Oct 29, 2019 | Excel Tips & Tricks

## Creating a quadratic equation in Excel

5x² + 6x + 1 = 0 => =5*POWER(x,2) + 6*x + 1 - y

## Using Goal Seek to solve quadratic equations in Excel

- Select the cell that contains the formula
- Open the Goal Seek dialog in Data > Data Tools > What-If Analysis > Goal Seek
- Set cell is the formula cell (It should be automatically selected)
- To value should be 0, which is the right end of the equation
- Select the cell of the x value to the By changing cell

## Results of Goal Seek

Note: Decrease the Maximum Change value to increase the precision .

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## Solving a Quadratic Equation

This is the general form of a quadratic equation:

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## Quadratic Equation Solver

[ back to excel vba sample code ].

ax 2 +bx+c , where a,b,c are constants.

The number of roots depends on the determinant of b 2 -4ac

If b 2 -4ac>0 then there are two roots

If b 2 -4ac=0 then there is only one root

If b 2 -4ac<0 then there is no root.

Copyright ® 2008 Dr.Liew Voon Kiong . All rights reserved

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A quadratic equation is of the form ax2 + bx + c = 0 where a ≠ 0. A quadratic equation can be solved by using the quadratic formula.

How to Solve a Quadratic Equation in Excel (Step-by-Step) · Step 1: Enter the Equation · Step 2: Find the First X Value Using Goal Seek · Step 3:

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Using Goal Seek to solve quadratic equations in Excel · Select the cell that contains the formula · Open the Goal Seek dialog in Data > Data Tools

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How to Use Excel to Solve a Quadratic Equation by Rick Hoban - January 27, 2013.

Clyde wonders if there is a function in Excel that solves quadratic equations. The short answer is that there is no such worksheet function

Explanation: · The format of the quadratic equation is as below: · ax2+bx+c , where a,b,c are constants. · The number of roots depends on the determinant of b2-4ac.