Equation Solver

Solve linear, quadratic, and polynomial equations

Enter Equation

Choose equation type and enter coefficients

a (coefficient of x²)

b (coefficient of x)

Solution

Enter coefficients and click Calculate

Solving Equations

Solving equations is the process of finding unknown values that make the equation true. Linear equations have one solution, while quadratic equations can have two solutions, one solution, or complex solutions. Understanding how to solve equations is fundamental in algebra and mathematics.

Types of Equations

Linear Equations: ax + b = 0

Linear equations are the simplest type of equations. They have one solution: x = -b/a (when a ≠ 0).

Example: 2x + 4 = 0 → x = -2

Quadratic Equations: ax² + bx + c = 0

Quadratic equations can be solved using the quadratic formula. The number of solutions depends on the discriminant (Δ = b² - 4ac).

Quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

• If Δ > 0: two real solutions

• If Δ = 0: one solution (double)

• If Δ < 0: two complex solutions

Practical Examples

Example 1: Linear equation

Solve the equation: 3x - 6 = 0

Solution: x = 6/3 = 2

Example 2: Quadratic equation

Solve the equation: x² - 5x + 6 = 0

Discriminant: Δ = 25 - 24 = 1 > 0, so two solutions: x₁ = 3 and x₂ = 2