About this tool
The Equation Solver takes any single-variable equation written as 'LHS = RHS' and finds every value of the variable that satisfies it. It parses both sides into polynomials, forms f(x) = LHS − RHS, and reduces to standard form aₙxⁿ + … + a₁x + a₀ = 0. A degree-1 equation is solved directly as x = −a₀/a₁. A degree-2 equation uses the quadratic formula x = (−b ± √(b² − 4ac)) / (2a); the sign of the discriminant b² − 4ac decides whether you get two real roots, one repeated root, or a complex-conjugate pair.
For degree 3 and 4 the solver applies the Rational Root Theorem — testing candidates ±p/q where p divides a₀ and q divides aₙ — and peels off each rational root by synthetic division, reducing what remains to a quadratic it can solve in closed form. When no rational roots remain and the degree is still 3 or higher, it switches to the Durand–Kerner (Weierstrass) iteration to locate all complex roots numerically, then rounds values that are extremely close to integers. Exact fractions are kept throughout via gcd reduction, and irrational quadratic roots are shown in simplified radical form.
Everything runs locally in your browser with an eval-free parser, so nothing you type is uploaded. Enter an equation such as '2x + 3 = 7' or 'x^2 - 5x + 6 = 0', optionally name the variable, and read the standard form, the method applied, and the full root list with decimal approximations.