Quadratic Formula Calculator

Use this quadratic formula calculator to solve any quadratic equation in the form ax² + bx + c = 0. Get step-by-step solutions and find the roots instantly.

Quadratic Formula Calculator

Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0, then click Calculate to find the roots.

$ax^2 + bx + c = 0$

What is a Quadratic Equation?

A quadratic equation is a second-degree polynomial equation in a single variable x, where a, b, and c are constants, and a ≠ 0. The standard form is ax² + bx + c = 0.

Quadratic equations can have either one, two, or no real solutions, depending on the value of the discriminant (b² - 4ac). When graphed, a quadratic equation forms a parabola.

The Quadratic Formula

The quadratic formula provides a way to solve any quadratic equation:

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The expression under the square root (b² - 4ac) is called the discriminant (Δ) and determines the nature of the roots:

$\Delta = b^2 - 4ac$

If Δ > 0, there are two distinct real roots. If Δ = 0, there is one repeated real root. If Δ < 0, there are two complex conjugate roots.

Applications of Quadratic Equations

Physics

Used in projectile motion, free-falling objects, and many other physical phenomena that involve acceleration.

Engineering

Applied in structural analysis, electrical circuits, and optimization problems in various engineering disciplines.

Finance

Used in calculating compound interest, asset pricing models, and option pricing in financial mathematics.

Computer Science

Applied in algorithm analysis, computer graphics for parabolic curves, and machine learning models.

How to Use This Calculator

  1. Enter the coefficient a (the coefficient of x²) in the first input field.
  2. Enter the coefficient b (the coefficient of x) in the second input field.
  3. Enter the coefficient c (the constant term) in the third input field.
  4. Click 'Calculate' to solve the equation and see the step-by-step solution.