Math formulas

Algebra formulas

Solve equations and work with algebraic expressions using clearly explained formulas and conditions.

Formulas and calculators

Quadratic equation

Enter the coefficients a, b, and c to calculate the discriminant and all real or complex roots of ax² + bx + c = 0.

x = (-b ± √(b² - 4ac)) / 2a

Calculated quantities

a - quadratic coefficient · b - linear coefficient · c - constant term

How to choose the right formula

Quadratic equation

x = (-b ± √(b² - 4ac)) / 2a

When to use it: For a non-zero leading coefficient a, the discriminant Δ = b² - 4ac determines the number and form of the roots.
Calculated quantities: a - quadratic coefficient (1) · b - linear coefficient (1) · c - constant term (1)
Worked example: Equation with two real roots: Solve x² - 5x + 6 = 0.

What to check before calculating

Assumptions and conditions

The equation must first be written in the standard form ax² + bx + c = 0.
The leading coefficient a must be non-zero; otherwise the equation is linear rather than quadratic.
The solver reports complex conjugate roots when the discriminant is negative.
Coefficients must be finite real numbers. Very large or nearly cancelling values may be affected by floating-point rounding.

Common mistakes

Using the formula before moving all terms to one side of the equation.
Allowing a = 0 and treating a linear equation as quadratic.
Dropping the ± sign and reporting only one of two roots.
Substituting a negative coefficient without parentheses.