Algebra calculators

Algebra calculators come up most often in homework checking: you solved a quadratic by hand, want to verify; you set up a system of two equations, want to confirm the intersection; you're translating between log bases. The tools here handle those common cases with the formula shown alongside the answer, so you can see where your arithmetic diverged from the calculator's.

The quadratic equation solver takes the standard ax² + bx + c form and returns both roots (real or complex), the discriminant, the vertex, and the axis of symmetry. Complex roots are written in the conventional a ± bi form. The linear equation solver handles ax + b = c with full step-through. For two equations in two unknowns, the system solver uses Cramer's rule and reports consistent / dependent / inconsistent cases distinctly — useful for homework where the "no solution" or "infinite solutions" case matters.

The logarithm calculator evaluates log_b(x) in any base, including the special-case shortcuts for natural log (base e) and common log (base 10). For symbolic manipulation (factoring, expanding, simplifying expressions, derivatives, integrals), these calculators are not the right tool — Wolfram Alpha and SymPy handle that domain. These pages are for the numerical case where you have specific values and want the specific answer.