This tool solves three types of equation — linear, quadratic, and simultaneous — using standard algebraic methods, entirely in your browser.
A linear equation in the form ax + b = c has exactly one solution (as long as a isn't zero). Subtract b from both sides to get ax = c − b, then divide both sides by a to isolate x: x = (c − b) / a. If a is zero and b equals c, every value of x works; if a is zero and b doesn't equal c, there's no solution at all.
A quadratic equation ax² + bx + c = d is first rearranged to standard form ax² + bx + (c − d) = 0, then solved with the quadratic formula: x = (−b ± √(b² − 4ac)) / 2a. The part under the square root, b² − 4ac, is the discriminant. A positive discriminant means two distinct real roots, zero means one repeated real root, and a negative discriminant means no real roots — only a pair of complex roots, which this tool can reveal separately.
For two equations in two unknowns (a₁x + b₁y = c₁ and a₂x + b₂y = c₂), Cramer's Rule finds x and y using determinants. The main determinant D = a₁b₂ − a₂b₁ tells you whether a unique solution exists — if D is zero, the lines are either parallel (no solution) or identical (infinite solutions). Otherwise, x = Dx / D and y = Dy / D, where Dx and Dy are determinants formed by swapping the constants into the x and y columns respectively.