What you can solve
Linear equations like 3(x − 1) = 2x + 4, quadratics, cubics and polynomials up to degree 24, with real and complex roots. Systems of linear equations with two to six unknowns, written one per line. And single-unknown equations with functions, such as cos(x) = x or x^2 = 2^x, which are solved to about twelve significant figures.
How the working is done
Linear equations are rearranged step by step. Quadratics use the formula, with the discriminant shown and square roots simplified, so you see √8 become 2√2. For cubics and higher, the solver tests every possible rational root p/q, divides out each one it finds, and finishes with the quadratic formula when it can. Systems are written as an augmented matrix and reduced with row operations in exact fractions, then checked by substituting back.
When the answer is a decimal
Some roots have no tidy exact form, like the real root of x³ = 2. Those are found numerically and marked with ≈. Equations with sin, log or roots are scanned for sign changes between the two search limits, then each root is pinned down with Newton’s method, falling back to halving the interval when a step jumps too far. If you expect a root outside the range, widen it. Everything runs in your browser and nothing you type is sent anywhere.