Solve linear, quadratic, cubic and systems of equations step-by-step with full working.
An equation solver finds the roots (values of the variable that make the equation true) for linear, quadratic, cubic, and quartic polynomial equations. The solver also handles systems of linear equations using Gaussian elimination.
Polynomial equations are the foundation of almost every applied math problem — from physics motion equations to chemistry equilibria to engineering design. Hand-solving anything beyond a quadratic is tedious and error-prone; a computational solver is the standard tool.
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Inputs: Solve x² − 5x + 6 = 0
A polynomial equation has complex roots whenever the discriminant is negative. Complex roots always come in conjugate pairs for polynomials with real coefficients. Quadratics either have 0 or 2 complex roots; cubics always have at least 1 real root; quartics can have 0, 2, or 4 complex roots.
Equations involving sin, cos, exp, or log generally cannot be solved algebraically — they require numerical methods like Newton-Raphson iteration or bisection. Our equation solver covers polynomial cases; for transcendental equations use a graphing approach to find approximate roots first.
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