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

Solution and Answer:

x=-0.333333
x=-0.5

Solution

6x²+5x+1=0
To solve, use the quadratic formula
x=-b ± b² - 4ac2a
Substitute your values for a, b, & c and solve
x=-5 ± 5² - 4·6·12·6
x=-5 ± 25 - 2412
x=-5 ± 112
Next, solve the radical
x=-5 ± 112
Then, reduce the problem
x=-512±112
x=-0.333333
x=-0.5


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 – 4ac2a

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 · 42 · 3

Begin solving the equation:

x = -8 ± 64 – 486
x = -8 ± 166
x = -8 ± 46

Next, reduce the fraction:

x = -86 ± 46
x = -43 ± 23

Thus, there are two solutions for x:

x = -43 + 23
x = -4323