Algebra Solver

An algebra solver automatically solves equations for an unknown variable (x). This tool supports two common equation types:

• Linear equations: ax + b = c → solve for x in one step
• Quadratic equations: ax² + bx + c = 0 → two roots via the quadratic formula

It shows full working, so it is perfect for checking homework or understanding the method.

1. Linear (ax + b = c): Rearrange → ax = c − b → x = (c − b) / a
2. Quadratic (ax² + bx + c = 0):
   • Δ = b² − 4ac (discriminant)
   • Δ > 0: two distinct real roots
   • Δ = 0: one repeated root
   • Δ < 0: two complex roots
   • x = (−b ± √Δ) / 2a

The discriminant (Δ = b² − 4ac) tells you the nature of roots before solving:

• Δ > 0: Two distinct real roots (the parabola crosses the x-axis twice)
• Δ = 0: One repeated root (the parabola just touches the x-axis)
• Δ < 0: No real roots — roots are complex numbers (a + bi form)

Example: x² − 5x + 6 = 0 → Δ = 25 − 24 = 1 → two roots: x = 3 and x = 2.

• School homework: Class 9–12 algebra problems
• Competitive exams: CAT, GMAT, GATE, JEE — equation solving
• Engineering: Solving for unknowns in design equations
• Finance: Break-even analysis, finding unknown rates
• Programming: Numerical root-finding problems