Equation Solver
Solve linear and quadratic equations step by step.
Linear Equation: ax + b = 0
Your Equation:
2x + (6) = 0
Solution
Solution
x = -3.0000
Steps:
1. 2x + (6) = 0
2. 2x = -6
3. x = -6 ÷ 2
4. x = -3.0000
Verification:
2 × -3.0000 + (6)
= 0.000000 ≈ 0 ✓
= 0.000000 ≈ 0 ✓
Equation Solving Methods
Linear Equations (ax + b = 0)
- Isolate x: x = -b/a
- Example: 2x + 6 = 0 → x = -6/2 = -3
Quadratic Equations (ax² + bx + c = 0)
Use the quadratic formula:
x = (-b ± √(b² - 4ac)) / 2a
Discriminant (Δ = b² - 4ac):
- Δ > 0: Two distinct real solutions
- Δ = 0: One repeated real solution
- Δ < 0: No real solutions (complex solutions)
Example: x² - 5x + 6 = 0
- a = 1, b = -5, c = 6
- Δ = (-5)² - 4(1)(6) = 25 - 24 = 1
- x = (5 ± √1) / 2 = (5 ± 1) / 2
- x₁ = 3, x₂ = 2