Quadratic Formula Calculator

Solve ax² + bx + c = 0 for real or complex roots using the quadratic formula.

⏱ Updated: 17 Sep 2026

Calculator

Free quadratic formula calculator: solve ax squared plus bx plus c equals zero for real or complex roots.

Discriminant (b² − 4ac) =
x₁
0
x₂
0
x (repeated root)
0
Complex Roots
± i

Enter the coefficients a, b, and c to solve a quadratic equation for x.

How to Use the Quadratic Formula Calculator

Coefficients a, b, and c plug straight into the formula — enter 0 for c if there's no constant term, since the field doesn't assume a default.

x = (−b ± √(b² − 4ac)) ÷ (2a)

Plug in a, b, and c from any ax² + bx + c = 0 and this solves for x — no factoring required, no guessing. Take x² − 3x − 4 = 0: a=1, b=−3, c=−4 gives x = (3 ± √25) ÷ 2, or x = 4 and x = −1.

The part under the square root, b² − 4ac, is the discriminant, and its sign tells you what you're getting before you finish the arithmetic. Positive means two distinct real roots. Zero means one repeated root — both branches of the ± collapse to the same value. Negative is where it gets interesting: two complex roots, and graphically, a parabola that never touches the x-axis at all, staying entirely above or entirely below it. The complex numbers the formula spits out in that case are real answers, just not ones you'll see as x-intercepts on a graph.

a can't be zero — without it the x² term vanishes and you're left with a linear equation, solved by isolating x directly rather than reaching for this formula.