# Quadratic Formula Calculator – with Steps to Solve

Enter the coefficients from a quadratic equation to solve for x using the quadratic formula.

## Result:

### Solution

## On this page:

## How to Use the Quadratic Formula

The quadratic formula can be used to calculate the solution for x in a quadratic equation. The quadratic formula uses numerical coefficients from a quadratic equation to allow you to solve for the value of x.

Given a quadratic equation of the form *ax² + bx + c = 0*, the quadratic formula looks like this:

x = -b ± b² – 4ac / 2a

Thus, the value of *x* is equal to *-b* plus or minus the square root of *b* squared minus 4 times *a* times *c* over 2 times *a*, where a is not equal to 0.

When the discriminant *b² – 4ac* is equal to 0 then there will be a single solution for *x*, otherwise there will be 2 possible solutions for *x*.

To use the quadratic formula, replace *a*, *b*, and *c* with the coefficients from the *ax² + bx + c = 0* equation, then solve.

The value of *a* cannot be equal to zero as that would mean the formula is missing the *x²*, which would mean it’s not a quadratic.

Let’s solve the equation

Start by substituting the coefficients into the formula:

x = -8 ± 8² – 4 · 3 · 4 / 2 · 3

Begin solving the equation:

x = -8 ± 64 – 48 / 6

x = -8 ± 16 / 6

x = -8 ± 4 / 6

Next, simplify the fraction:

x = -8 / 6 ± 4 / 6

x = -4 / 3 ± 2 / 3

Thus, there are two solutions for *x*:

x = -4 / 3 + 2 / 3

x = -4 / 3 – 2 / 3

You might be interested in using our vertex form calculator to convert from quadratic to vertex form.