Quadratic Formula Calculator – with Steps to Solve
Enter the coefficients from a quadratic equation to solve for x using the quadratic formula.
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.