Solve any quadratic equation ax² + bx + c = 0 instantly. Find real and complex roots.
Solve ax² + bx + c = 0
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Quadratic equations feel purely academic until you realize they describe projectile motion, satellite dish curvature, suspension bridge cables, and profit-maximization problems in business — the parabolic shape appears constantly in physics and engineering.
The discriminant (b²-4ac) tells you the nature of the solutions before you even solve the equation — positive means two real solutions, zero means exactly one repeated solution, and negative means the solutions are complex numbers (involving imaginary numbers), which has practical implications for whether a real-world scenario the equation models is even physically possible.
In physics, quadratic equations model anything involving constant acceleration — a thrown ball's height over time, a car's stopping distance, or a rocket's trajectory all follow quadratic relationships, making this "abstract" math directly applicable to real motion.
Use the calculator above to solve any quadratic equation instantly, including finding the vertex (useful for identifying maximum height or minimum cost in optimization problems) — practical for coursework, engineering calculations, or satisfying curiosity about a real-world parabolic scenario.