Solve linear and quadratic equations with step-by-step solutions
Solve four kinds of equations from a simple form: linear (ax + b = 0), quadratic (ax^2 + bx + c = 0), cubic (ax^3 + bx^2 + cx + d = 0), and a system of two linear equations in x and y. You enter the coefficients in labeled fields and pick the equation type; the solver returns the roots along with a step-by-step breakdown.
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You need the roots of x² − 5x + 6 = 0 and want to confirm your factoring by hand.
Equation
x^2 - 5x + 6 = 0
Solutions
x = 2 or x = 3 (discriminant 1 > 0 → two real roots)
The solver applies the quadratic formula and reports the discriminant, so you also learn why there are two real roots rather than one or none. It handles linear, quadratic, and systems, showing steps so it teaches rather than just answers.
Solve four kinds of equations from a simple form: linear (ax + b = 0), quadratic (ax^2 + bx + c = 0), cubic (ax^3 + bx^2 + cx + d = 0), and a system of two linear equations in x and y. You enter the coefficients in labeled fields and pick the equation type; the solver returns the roots along with a step-by-step breakdown.
Linear equations are solved directly as x = -b/a. Quadratics use the quadratic formula, reporting two real roots, one repeated root, or a complex conjugate pair (a +/- bi) depending on the sign of the discriminant b^2 - 4ac. Cubics are reduced to a depressed cubic and solved with Cardano's formula when there is one real root, or the trigonometric method when there are three real roots; repeated-root cases are handled separately. The 2x2 system is solved with Cramer's rule, computing the determinant of the coefficient matrix and detecting parallel lines (no solution) or coincident lines (infinite solutions). Every solver lists its intermediate steps so you can follow the method, not just copy the answer.
Solve assigned linear, quadratic, and cubic equations and review the steps to understand the method.
Quickly find the roots of a polynomial up to degree three without rearranging by hand.
Practice solving equations and verify your answers before an exam.
Solve two simultaneous linear equations and see how Cramer's rule produces x and y.
Yes, for two variables: choose the system mode and enter the coefficients of two linear equations (a1x + b1y = c1 and a2x + b2y = c2). The solver applies Cramer's rule and also detects parallel or coincident lines.
For quadratics with a negative discriminant, the solver returns the complex conjugate roots in a +/- bi form.
Single equations up to degree three (cubic). There is no general polynomial solver beyond cubic.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.