Quadratic Equation Calculator Online - Solve Equations Instantly

Solve any quadratic equation (ax² + bx + c = 0) quickly with step-by-step solutions using our calculator.

Quadratic Equation
Enter coefficients for ax² + bx + c = 0
- 5x + 6 = 0

Quadratic Formula

x = (-b ± √(b² - 4ac)) / 2a
Solution
Roots and properties of the quadratic equation

Roots:

x₁ =0

Properties:

Discriminant (Δ):0.0000
Vertex:(0.0000, 0.0000)
Axis of Symmetry:x = 0.0000
Opens:Upward

Step-by-Step Solution:

1. Identify: a = 1, b = -5, c = 6

2. Calculate discriminant: Δ = b² - 4ac = -5² - 4(1)(6) = 0

3. Apply quadratic formula:

x = (--5 ± √0) / (2 × 1)

4. x₁ = (--5 + √0) / 2 = 0

5. x₂ = (--5 - √0) / 2 = 0

Understanding Quadratic Equations

A quadratic equation is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where:

  • a is the coefficient of x² (cannot be zero)
  • b is the coefficient of x
  • c is the constant term

The Quadratic Formula

The quadratic formula x = (-b ± √(b² - 4ac)) / 2a provides the solution to any quadratic equation.

The Discriminant

The discriminant (Δ = b² - 4ac) determines the nature of the roots:

  • Δ > 0: Two distinct real roots
  • Δ = 0: One repeated real root
  • Δ < 0: Two complex conjugate roots
Applications of Quadratic Equations

Physics & Engineering

  • Projectile motion calculations
  • Optimization problems
  • Circuit analysis
  • Structural engineering

Business & Economics

  • Profit maximization
  • Cost analysis
  • Revenue optimization
  • Break-even analysis