Quadratic equations are a fundamental part of algebra and often appear in math homework, tests, and real-world applications. Our Quadratic Equation Solver helps you quickly and accurately find the roots of any quadratic equation. Just input your coefficients (a, b, and c), and instantly discover the equation’s solutions—whether they’re real or complex.
A quadratic equation takes the form ax² + bx + c = 0, where "a" cannot be zero. Quadratic equations can have two solutions, one solution, or no real solutions at all, depending on the discriminant, calculated as D = b² - 4ac.
The calculator uses the quadratic formula:
x = [-b ± √(b² - 4ac)] / (2a)
If the discriminant (D) is positive, you'll get two real solutions. If it's zero, there's one real solution (known as a double root). If negative, the calculator gives you two complex solutions.
Quadratic equations can yield different types of roots:
Use our Quadratic Equation Solver to simplify your math problems and strengthen your algebra skills. Solve equations instantly and gain confidence in your mathematical abilities.
Compute the QR decomposition of a 2x2 or 3x3 matrix using the Gram-Schmidt process.
Compute the Minkowski distance between two points in 2D or 3D for any positive p.
Apply Aitken's delta-squared process to improve the convergence of a sequence.