# Quadratic Formula Calculator – with Steps to Solve

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

ax² + bx + c = 0

## Result:

x=-0.333333
x=-0.5

### Solution

6x²+5x+1=0
To solve, use the quadratic formula
x=-b ± b² - 4ac / 2a
Substitute your values for a, b, & c and solve
x=-5 ± 5² - 4·6·1 / 2·6
x=-5 ± 25 - 24 / 12
x=-5 ± 1 / 12
Next, solve the radical
x=-5 ± 1 / 12
Then, reduce the problem
x=-5 / 12±1 / 12
x=-0.333333
x=-0.5
Learn how we calculated this below

## 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 , which would mean it’s not a quadratic.

Let’s solve the equation 3x² + 8x + 4 = 0 using the quadratic formula as an example.

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 / 32 / 3

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