Quadratic Formula Calculator
Solve ax² + bx + c = 0 for real or complex roots.
Assumptions used in this calculation
- Complex roots: When the discriminant is negative, roots are reported in a + bi complex form rather than being treated as no solution.
About this calculator
Solving a quadratic equation by hand means correctly identifying a, b and c, computing the discriminant, and then handling three different outcomes depending on its sign, which is where sign errors and square-root mistakes most commonly creep in, especially when the discriminant turns out negative and the roots become complex. This calculator takes the coefficients a, b and c from ax² + bx + c = 0 and applies the quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a directly, evaluating the discriminant (b² − 4ac) to determine whether the result is two distinct real roots, one repeated real root, or a pair of complex conjugate roots, and formats the answer accordingly rather than returning an error when the discriminant is negative. It requires a nonzero a, since a = 0 collapses the equation to a linear one outside the formula's scope, and it removes the arithmetic risk of a dropped negative sign under the square root.
Worked example
x² − 5x + 6 = 0
Result: x₁ = 3, x₂ = 2
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