Equation Solver

Solve equations of all types: linear, quadratic, cubic, polynomial, systems of equations, exponential, logarithmic, and absolute value. Detailed step-by-step solutions with explanations included.

This calculator dispatches to one of nine independent solving routines based on Equation Type (lines 1168-1227): linear (isolation method), quadratic (the quadratic formula), cubic, degree-5 polynomial, 2×2 and 3×3 linear systems (Cramer's rule per the formula field), exponential, logarithmic, and absolute-value equations. Each routine reads only its own dedicated set of coefficient fields — the quadratic routine, for example, never looks at Third Number coefficients or system-of-equations inputs — so with any equation type selected, the roughly thirty coefficient fields belonging to the other eight types have zero effect on the result, a fact confirmed directly: at the default Linear type, every coefficient field belonging to the other eight equation types (Quadratic's a, Cubic's a, Absolute Value's c, and so on) shows no measurable effect on Solution 1 at all. In Linear mode, ax + b = c is solved as x = (c − b) / a (line 111); at the default coefficients (a=2, b=3, c=7), Result (c) has the largest effect on Solution 1, followed by a and then b — and since a, b, and c are all positive at these defaults, raising c raises the solution, while raising either a or b lowers it. This calculator does not use numerical approximation for linear, quadratic, or cubic equations — those have closed-form solutions — but Polynomial mode, along with root-finding elsewhere on the site's Graphing Calculator, does rely on numerical methods for degrees where no closed-form formula is used. Linear mode has its own special case: when a = 0, the equation becomes 0x + b = c, which the solver correctly recognizes as either an identity (true for every x, if b = c) or a contradiction (true for no x, if b ≠ c) rather than attempting to divide by 0 (lines 51-97).