About the quadratic formula calculator
This free quadratic formula calculator solves quadratic equations in the form ax² + bx + c = 0. You enter the coefficients a, b, and c, and the calculator uses the quadratic formula to find all roots—whether two real roots, one repeated root, or two complex roots. It also shows the discriminant (b² − 4ac), which tells you how many real solutions exist. No sign-up or download is required; the tool works in your browser and is designed to be mobile-friendly and responsive.
The quadratic formula is x = (−b ± √(b² − 4ac)) / (2a). It works for any quadratic equation with real coefficients. When the discriminant is positive, there are two distinct real roots; when it is zero, there is one repeated root (a double root); when it is negative, there are two complex conjugate roots. This calculator evaluates the formula and displays the results in decimal form, so you can check homework, study for tests, or solve problems quickly without doing the algebra by hand.
Quadratic equations appear everywhere: in physics (projectile motion, springs), engineering (optimization, control theory), finance (certain profit models), and of course in algebra and pre-calculus courses. Knowing how to use the quadratic formula is essential for solving problems that cannot be factored easily. This calculator accepts decimal and negative coefficients, so you can handle equations like 2.5x² − 3x + 1.2 = 0 or −x² + 4x − 3 = 0. Just ensure a ≠ 0; otherwise the equation is not quadratic.
Use this quadratic formula calculator for homework, exam prep, or quick verification of solutions. It is free, responsive on phones and tablets, and shows the discriminant so you can connect the formula to the number and type of roots. For factoring or completing the square instead, try our other algebra tools. This page focuses solely on solving ax² + bx + c = 0 using the quadratic formula.