⭐ Starlight Tools / Quadratic Equation Calculator

Quadratic Equation Calculator

Solve quadratic equations of the form ax2 + bx + c = 0 and see the step-by-step solution.

Solution:
Calculation Steps:
Enter coefficients and click "Solve Equation" to see the steps.

Understanding Quadratic Equations

A **quadratic equation** is a polynomial equation of the second degree. The general form is:

ax2 + bx + c = 0

Where 'x' represents an unknown, and 'a', 'b', and 'c' are coefficients, with 'a' not equal to 0. If a = 0, the equation becomes linear.

The Quadratic Formula

The solutions for 'x' in a quadratic equation are given by the **quadratic formula**:

x = [-b ± √(b2 - 4ac)] / 2a

This formula can be used to find the roots (or solutions) of any quadratic equation.

The Discriminant (Δ)

The term inside the square root, b2 - 4ac, is called the **discriminant** (often denoted by the Greek letter delta, Δ). It tells us about the nature of the roots:

  • If Δ > 0: There are two distinct real roots.
  • If Δ = 0: There is exactly one real root (a repeated root).
  • If Δ < 0: There are two distinct complex roots (involving imaginary numbers).

How This Tool Works

This calculator takes the coefficients 'a', 'b', and 'c' as input. It then applies the quadratic formula to determine the roots. It also generates a step-by-step breakdown of the calculation, showing:

  • The substituted values into the quadratic formula.
  • The calculation of the discriminant (Δ).
  • The simplification of the square root term.
  • The final calculation for x1 and x2.
  • Handling of real and complex roots.

All calculations are performed client-side in your browser, ensuring privacy.