Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a). Discriminant: Δ = b² − 4ac. If Δ<0, roots are complex.
Quadratic equations of the form ax² + bx + c = 0 show up in physics, engineering, optimization, and algebra practice. The Quadratic Equation Solver finds roots quickly and clearly.
This calculator uses the quadratic formula and handles three key cases: two real roots (positive discriminant), one real repeated root (zero discriminant), and complex roots (negative discriminant).
To help you verify results, the calculator shows the discriminant (Δ = b² − 4ac) and explains how it determines the type of roots.
If you’re learning quadratic equations, the worked examples demonstrate how changing a single coefficient affects the discriminant and therefore the solutions.
Even if you’re using the solver for homework or quick checks, the structured output is designed for readability. That reduces the chance of mixing up signs or misplacing coefficients.
Example inputs and outputs using the calculator logic.
Quick links to similar calculators.
Answers to help you use the calculator correctly.
It determines how many real roots there are: Δ>0 (two distinct real roots), Δ=0 (one repeated root), Δ<0 (two complex roots).
Then the equation isn’t quadratic. The solver expects a≠0.
This depends on implementation. The solver typically outputs rounded decimals for complex parts and real roots for readability.
Complex roots include real and imaginary parts. They occur when the parabola does not intersect the x-axis.
Yes when Δ=0, meaning both solutions are the same.