Quadratic Formula Calculator | Solve Equations Step-by-Step
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Enter Coefficients

ax² + bx + c = 0
Coefficient a
Coefficient b
Coefficient c
Quick Examples

Step-by-Step Solution

Step 1: Calculate Discriminant (Δ)
Formula: Δ = b² - 4ac
Δ = ?
Step 2: Nature of Roots
Determining based on discriminant value...
Step 3: Apply Quadratic Formula
Formula: x = (-b ± √Δ) / 2a
x = ?
Final Result
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Graph will appear here after calculation

Calculation History

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What is the Quadratic Formula?

The quadratic formula is a universal method used to solve quadratic equations. A quadratic equation is a second-order polynomial equation in a single variable x, written as:

ax² + bx + c = 0

Where:

  • a, b, and c are real numbers and a ≠ 0.
  • x is the unknown variable (the root).

How to Use This Calculator

Our Quadratic Formula Calculator makes it easy to find the roots of any quadratic equation in three simple steps:

  1. Enter the value of coefficient a (must not be 0).
  2. Enter the value of coefficient b.
  3. Enter the value of coefficient c.
  4. Click Solve Equation to see the result, graph, and step-by-step calculation.

Understanding the Discriminant (Δ)

This tool automatically calculates the discriminant (Δ = b² - 4ac) to tell you the nature of the roots:

  • If Δ > 0: Two distinct real roots.
  • If Δ = 0: One repeated real root.
  • If Δ < 0: Two complex (imaginary) roots.