Two regular-number answers
For x² − 5x + 6 = 0, the number under the square root is 1, so the two answers for x are 3 and 2.
Find the value of x
Quadratic formula calculator
Copy the a, b, and c numbers from your equation to find the possible values of x.
Calculated in your browser
Formula and steps included
No account. No signup.
Optional learning Learn how this math works See the formula, definitions, and step-by-step method.
Formula
The quadratic formula
For ax² + bx + c = 0 and a ≠ 0: x = (−b ± √(b² − 4ac)) / (2a)
The quadratic formula solves equations written as ax² + bx + c = 0 when a is not zero. The ± sign means calculate once with plus and once with minus, so there can be two answers for x.
The number under the square root, b² − 4ac, is called the discriminant. A positive number gives two everyday-number answers, zero gives one repeated answer, and a negative number gives two answers that use i.
How to use the formula
Find a, b, and c
Move everything to one side so the other side is 0, then copy the three labeled numbers from ax² + bx + c = 0.
Find the number under the square root
Calculate b² − 4ac. This number is also called the discriminant.
Finish and check both answers
Put the numbers into the formula, calculate once with plus and once with minus, then try each answer in the original equation.
Worked examples
Quadratic formula examples
Two answers that use i
For 2x² + 4x + 5 = 0, the number under the square root is −24. A negative number there makes answers that use i, a special number for square roots of negative numbers: x = −1 ± (√6 / 2)i.
Common questions
Quadratic formula FAQ
What does the discriminant tell me?
It tells you what kind of answers to expect: two everyday-number answers when positive, one repeated answer when zero, and two answers that use i when negative.
Can a equal zero in the quadratic formula?
No. If a is zero, the x² term disappears and the equation is linear or constant, so the quadratic formula does not apply.
Why does the formula have plus or minus?
A quadratic can cross the x-axis at two points. Evaluating both signs finds both roots when they are distinct.
Are my equation coefficients uploaded?
Your equation numbers stay in your browser and are not saved by default or uploaded. Use Save on this device to keep them here, or download a backup file.