🔢 Math Calculator

📐 How It Works

Solves ax² + bx + c = 0 using the quadratic formula. Gives two solutions (real or complex), or one repeated root when the discriminant equals zero.

🔢 Worked Examples

• x²−5x+6=0 → x=2, x=3
• x²+4=0 → no real roots (Δ<0)
• 4x²−12x+9=0 → x=1.5 (repeated root)
• 2x²+3x−2=0 → x=0.5, x=−2

📋 Common Use Cases

• Physics — projectile trajectory
• Engineering — beam deflection equations
• Finance — break-even analysis (revenue = cost)
• Architecture — parabolic arch design

💡 Did You Know?

The quadratic formula was known to Babylonian mathematicians around 2000 BCE — they solved it geometrically using "completing the square" without algebraic notation.

⚠️ Common Mistake

Forgetting the ± — there are usually TWO solutions. Also, when Δ < 0, the equation has two complex conjugate roots (a+bi and a−bi), not "no solution."