Equation Solver
Solve linear and quadratic equations step by step.
Enter your equation coefficients to find the solution with detailed working.
This calculator solves three types of algebraic equations step by step, showing the method used to reach the answer.
Linear Equation: ax + b = 0
x = -b / a
Here a is the coefficient of x and b is the constant term. To solve, isolate x by subtracting b and dividing by a.
Quadratic Equation: ax² + bx + c = 0
x = (-b ± √(b² - 4ac)) / 2a
Here a is the coefficient of x², b is the coefficient of x, and c is the constant. The expression under the square root, b² - 4ac, is called the discriminant. If it is positive, there are two real solutions. If zero, one repeated solution. If negative, two complex solutions.
System of Two Linear Equations:
a₁x + b₁y = c₁ and a₂x + b₂y = c₂
Solved using Cramer’s Rule, which uses determinants: D = a₁b₂ - a₂b₁. If D is not zero, there is a unique solution for both x and y.
When to use this calculator: Use it for homework, test preparation, or any situation requiring algebraic solutions. Engineers, scientists, and students regularly solve these equation types.
Practical example: Solve 2x² - 5x + 3 = 0. The discriminant = 25 - 24 = 1 (positive, so two real roots). x₁ = (5 + 1) / 4 = 1.5 and x₂ = (5 - 1) / 4 = 1.0.
Common mistakes: For quadratics, remember that a must not be zero (otherwise it is a linear equation). For systems, if the determinant is zero, the lines are parallel (no solution) or identical (infinite solutions). Always double-check signs when entering negative coefficients.