Quadratic Equation Solver

A quadratic equation has the form ax² + bx + c = 0, where a can't be zero — it's one of the core equation types covered in algebra, showing up anywhere a relationship involves a squared term: projectile motion, area problems, and plenty of standardized-test questions. Solving one by hand means correctly applying the quadratic formula and simplifying a square root, which is easy to get wrong under time pressure. This tool does the arithmetic instantly so you can check your work or move straight to interpreting the answer.

The key to understanding the result is the discriminant — the b² − 4ac term under the square root. When it's positive, the equation has two distinct real solutions. When it's exactly zero, both solutions land on the same value, so there's only one repeated root. When it's negative, there's no real number that satisfies the equation — the two solutions are a complex conjugate pair instead, which this tool reports explicitly rather than showing a real number that isn't actually a valid answer.

Enter your three coefficients exactly as they appear in your equation, including their signs — for 2x² − 5x + 3 = 0, that's a = 2, b = −5, c = 3. The one input that has to follow a rule is a: it can't be zero, since a missing x² term means the equation isn't quadratic in the first place.