Solve a quadratic with the formula
Enter a, b, c from ax² + bx + c = 0 to get both roots — or the complex pair — plus the discriminant and vertex.
Tools used in this guide
The job
A quadratic is set before you — physics homework, a projectile height, an optimization problem, or checking worked answers. The solver applies the quadratic formula and reports the roots, the discriminant, and the parabola's vertex.
How to do it
Write the equation in standard form ax² + bx + c = 0 first — move every term to one side. Enter the three signed coefficients (for x² − 3x + 2 = 0, that is a=1, b=−3, c=2) and solve.
Worked example
x² − 3x + 2 = 0 gives discriminant 1 and roots x = 1 and x = 2 — check by factoring: (x−1)(x−2). With a = 0 the tool says so and solves the remaining linear equation instead.
Limits
A negative discriminant produces the complex pair (real ± imaginary i), which some courses do not cover yet. Double precision handles coefficients to ±10¹⁵, but extreme size ratios can drop trailing digits — treat the last digits of a huge-discriminant result with care.