Equation Solver

Solve linear equations (ax + b = c) and quadratic equations (ax² + bx + c = 0).

Equation Type

Understanding Equations

An equation is a mathematical statement that asserts the equality of two expressions. Solving an equation means finding the value(s) of the variable(s) that make the statement true.

Linear Equation (ax + b = c)

x = (c - b) / a

A linear equation has at most one solution.

Quadratic Equation (ax² + bx + c = 0)

x = [-b ± √(b² - 4ac)] / 2a

A quadratic equation can have two, one, or no real solutions, depending on the discriminant (b² - 4ac).

Equation Examples

Equation Type Equation Solutions
Linear2x + 4 = 10x = 3
Linear5x - 1 = 9x = 2
Quadraticx² - 5x + 6 = 0x = 2, x = 3
Quadraticx² + 4x + 4 = 0x = -2
Quadraticx² + 1 = 0No real solutions

Frequently Asked Questions

What is an equation?

An equation is a mathematical statement that asserts the equality of two expressions. It typically contains one or more variables.

What is a linear equation?

A linear equation is an algebraic equation in which each term has an exponent of 1 and the graphing of the equation results in a straight line. It has at most one solution.

What is a quadratic equation?

A quadratic equation is a polynomial equation of the second degree, meaning it contains at least one term in which the unknown quantity is squared but no higher. Its general form is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0. It can have up to two solutions.