Solve linear equations (ax+b=0), quadratic equations (ax²+bx+c=0 with discriminant Δ and complex roots), and 2x2 systems with step-by-step solutions.
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The Equation Solver provides step-by-step solutions for fundamental algebraic equations: linear equations (ax + b = 0), quadratic equations (ax² + bx + c = 0) including real and complex conjugate roots, and 2×2 systems of linear equations using Cramer’s Rule.
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, \quad \Delta = b^2 - 4acIf Δ > 0, there are two distinct real roots; if Δ = 0, one repeated root; if Δ < 0, two complex conjugate roots p ± qi.
Scenario: Solving x² - 5x + 6 = 0
Identify coefficients: a = 1, b = -5, c = 6.
Discriminant: Δ = (-5)² - 4(1)(6) = 25 - 24 = 1.
Apply formula: x = (5 ± √1) / 2 = (5 ± 1) / 2.
Roots: x₁ = 3, x₂ = 2.
When Δ < 0, the equation has no real solutions. Instead, it has two complex conjugate roots containing the imaginary unit i (where i = √(-1)).
Cramer’s Rule computes the determinant of the coefficient matrix D = a₁b₂ - a₂b₁. If D ≠ 0, the unique solutions are x = D_x / D and y = D_y / D.
If a = 0, the equation reduces to a first-degree linear equation (bx + c = 0), which has a single solution x = -c/b.
Yes, all positive, negative, integer, and decimal coefficients are supported.
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