Quadratic Formula Calculator
Calculate your Quadratic solution in seconds with the free Quadratic Formula Calculator. No registration needed.
Coefficients
Roots
What is a Quadratic Formula Calculator?
A quadratic formula calculator solves equations of the form ax2 + bx + c = 0. It uses the quadratic formula to find real and complex roots, handling all cases including linear equations when a = 0.
How to use the quadratic formula manually (the formula)
The quadratic formula is: x = (−b ± √(b2 − 4ac)) / (2a). The discriminant (b2 − 4ac) determines the nature of the roots. Plug in a, b, and c and solve.
Example calculation
Solve x2 − 3x + 2 = 0 (a = 1, b = −3, c = 2). Discriminant = (−3)2 − 4(1)(2) = 9 − 8 = 1. x = (3 ± 1) / 2. Roots: x = 2 and x = 1.
Common mistakes
- Forgetting to change the sign of b — The formula is −b, not b. If b = −3, then −b = 3.
- Miscomputing the discriminant — Remember b2 − 4ac, not b2 − 4a + c or other variants.
- Forgetting that a cannot be zero — If a = 0, the equation is not quadratic and the formula does not apply.
Frequently asked questions
How do I use the quadratic formula?
x = (−b ± √(b2 − 4ac)) / (2a).
What is the discriminant?
b2 − 4ac; tells the nature of roots.
What if a is 0?
It becomes a linear equation.
What are complex roots?
Roots involving i when discriminant is negative.
How do I check my answer?
Substitute roots back into the equation.
Can I use this calculator on mobile?
Yes, works on all devices.