Every Toolkit

Quadratic Equation Solver

Solve ax² + bx + c = 0 and display both real and complex roots

Equation: ax² + bx + c = 0

Enter coefficients a, b, and c

Your Equation:
x² - 5x + 6 = 0

Step-by-Step Solution

Step 1: Identify coefficients
a = 1, b = -5, c = 6
Step 2: Calculate discriminant
Δ = b² - 4ac = (-5)² - 4(1)(6)
Δ = 1
Step 3: Determine root type
Δ > 0: Two distinct real roots
Step 4: Apply quadratic formula
x = (-b ± √Δ) / (2a)

Solutions

Two distinct real roots

Root 1 (x₁)
3
Root 2 (x₂)
2
Discriminant (Δ)
1
Vertex
(2.5, -0.25)

Parabola Graph

Visual representation of the quadratic function

xy
RootsVertexParabola

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About Quadratic Equation Solver

Solve Quadratic Equations

This calculator solves quadratic equations of the form ax² + bx + c = 0 using the quadratic formula. It handles all types of roots: real distinct, real equal, and complex conjugate roots. Includes step-by-step solutions and visual graph representation.

Features

  • Solve any quadratic equation
  • Real and complex root support
  • Step-by-step solution breakdown
  • Discriminant calculation
  • Vertex calculation
  • Interactive parabola graph
  • Visual root markers
  • Equation preview
  • High precision results
  • Example equation included

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Discriminant (Δ)

Δ > 0: Two distinct real roots
Δ = 0: One repeated real root (vertex on x-axis)
Δ < 0: Two complex conjugate roots

How to Use

  1. Enter coefficient 'a' for x² term (must not be zero)
  2. Enter coefficient 'b' for x term
  3. Enter constant 'c'
  4. View the equation preview
  5. Check the calculated roots and discriminant
  6. Review the step-by-step solution
  7. Examine the parabola graph

Common Applications

  • Algebra homework and assignments
  • Physics projectile motion problems
  • Engineering calculations
  • Optimization problems
  • Mathematical modeling