Algebra Calculator
Solve linear equations, quadratic equations, and systems of equations step-by-step. Find roots, discriminants, and variables instantly with our free algebra solver.
Algebra Equation Solver
Enter coefficients to solve for variables
Choose the type of algebraic equation you want to solve
Solution & Steps
Variables, roots, and step-by-step breakdown
Select an equation type, enter your coefficients, and click Solve to see the step-by-step solution.
Essential Algebra Formulas
Common algebraic formulas and expressions used to solve equations and simplify expressions.
| Formula Name | Equation / Expression | Description |
|---|---|---|
| Linear Equation | ax + b = c | Solves for a single variable with degree 1 |
| Quadratic Formula | x = (-b ± √(b² - 4ac)) / 2a | Finds roots of a degree 2 polynomial |
| Slope-Intercept | y = mx + b | Defines a straight line with slope m and y-intercept b |
| Point-Slope | y - y₁ = m(x - x₁) | Equation of a line through point (x₁, y₁) with slope m |
| Difference of Squares | a² - b² = (a - b)(a + b) | Factors a binomial of two perfect squares |
| Perfect Square | (a ± b)² = a² ± 2ab + b² | Expands or factors a squared binomial |
Algebra Solver FAQ
Everything you need to know about solving algebraic equations and using this calculator.
To solve a linear equation like ax + b = c, your goal is to isolate the variable x. First, subtract b from both sides to get ax = c - b. Then, divide both sides by a to find x = (c - b) / a. This calculator performs these steps automatically and shows you the exact solution.
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a. It provides the solutions to any quadratic equation in the form ax² + bx + c = 0. The ± symbol means you calculate the formula twice: once with addition and once with subtraction, giving you up to two distinct roots (x₁ and x₂).
A system of equations consists of two or more equations with the same variables. For a 2x2 system (a₁x + b₁y = c₁ and a₂x + b₂y = c₂), you can use methods like substitution, elimination, or Cramer's Rule. This calculator uses the determinant method (Cramer's Rule) to instantly find the unique values of x and y that satisfy both equations simultaneously.
The discriminant is the expression under the square root in the quadratic formula: Δ = b² - 4ac. It tells you the nature of the roots without fully solving the equation. If Δ > 0, there are two distinct real solutions. If Δ = 0, there is exactly one real solution (a repeated root). If Δ < 0, there are no real solutions (two complex solutions).
Yes! You can enter any real number as a coefficient, including decimals (e.g., 2.5, -0.75). The calculator processes floating-point numbers and rounds the final output to 6 decimal places for readability.
If the discriminant (b² - 4ac) is negative, the equation has no real roots because you cannot take the square root of a negative number in the real number system. Instead, the solutions are complex numbers, involving the imaginary unit i (where i² = -1). The calculator will display the real and imaginary parts of the complex roots.