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About this tool
Solve linear, quadratic, and system of equations step-by-step with detailed explanations and visual graphing.
The Algebra Solver works out three kinds of equation and shows every line of the working: single-variable linear equations by isolating x, quadratics with the discriminant Δ = b² − 4ac and the quadratic formula, and two-equation systems in x and y by Cramer's rule. It reports the numeric answer alongside the exact fraction whenever the two differ, so 3x = 5 comes back as both 1.666667 and 5/3. It is aimed at students checking homework, where the steps matter more than the final number.
Open Algebra Solver on AltFTool — it loads instantly in your browser.
Pick a card under Equation Type: Linear Equation (ax + b = c), Quadratic Equation (ax² + bx + c = 0) or System of Equations for two equations and two unknowns.
Type your equation into the input field, such as 2x + 5 = 13 or 2x + y = 7, x - y = 2 for a system, or tap one of the five Sample Equations chips to load a ready-made one.
Press Solve or hit Enter to see the result badge - Solution Found, Two Solutions, Repeated Root, Complex Roots, No Solution or Infinite Solutions - with each variable's value and a numbered Step-by-Step Solution below it.
Coefficients identified, discriminant computed, roots substituted — not just the final value.
Answers are reduced with a GCD, so you get 5/3 rather than a rounded 1.666667.
Distinguishes a unique solution, a repeated root, two real roots, complex roots, no solution and infinitely many.
The sign of Δ = b² − 4ac decides the roots: Δ > 0 gives two distinct real roots, Δ = 0 gives one repeated real root at x = −b/2a, and Δ < 0 gives no real roots, only a complex conjugate pair. For x² + 2x + 5 = 0, Δ = 4 − 20 = −16, so the roots are complex.
By Cramer's rule. It computes the determinant D = a₁b₂ − b₁a₂, then Dx and Dy, and gives x = Dx/D and y = Dy/D. If D = 0 there is no unique solution, because the two lines are either parallel or the same line.
Plain text with x as the variable: 2x + 5 = 13 for linear, x^2 - 5x + 6 = 0 for quadratic (x² and x**2 both work), and two comma-separated equations like 2x + y = 7, x - y = 2 for a system. Spaces are ignored, and quadratics are read from the left-hand side with the right side taken as 0.
Yes. When every x term cancels out, the equation is no longer about x. If what remains is a false statement such as 5 = 3 there is no solution; if it reduces to 0 = 0 the equation is true for every x, which is infinitely many solutions. The solver labels both cases explicitly rather than returning an error.
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