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Quadratic Equation Calculator

The calculator find the solution for given quadratic equation.

Calculator

 

Results:

The quadratic equations are those equations that have highest exponent is 2, means as an equation of degree 2 as follows:
ax2 + bx + c = 0,

where

a, b, and c are real numbers and a cannot be 0.

For example:

x2 + 8x + 16 = 0 is a quadratic equation

where

a = 1, b = 8 and c = 16.

What is a Quadratic Equation?

A quadratic equation is an algebraic equation in which the highest power of the variable is 2. Because the variable is squared, the graph of the equation always forms a U-shaped curve called a parabola.

The standard form of a quadratic equation is:

ax² + bx + c = 0

Here:

  • a is the coefficient of x² (cannot be 0).
  • b is the coefficient of x.
  • c is the constant term.

For example:

2x² + 5x − 3 = 0

In this equation:

  • a = 2
  • b = 5
  • c = -3

What Does This Calculator Do?

The Quadratic Equation Calculator helps you solve equations quickly and accurately. Simply enter the values of a, b, and c, then click the Calculate button. The calculator finds the values of x that satisfy the equation.

It also shows a detailed step-by-step solution so you can understand every calculation instead of only seeing the final answer.

The calculator can:

  • ✔ Solve any quadratic equation.
  • ✔ Find both roots of the equation.
  • ✔ Calculate the discriminant.
  • ✔ Identify whether the roots are real or complex.
  • ✔ Show detailed calculation steps.
  • ✔ Help students learn the quadratic formula.
  • ✔ Save time and reduce calculation mistakes.

How to Use the Quadratic Equation Calculator

  1. Enter the value of a.
  2. Enter the value of b.
  3. Enter the value of c.
  4. Click the Calculate button.
  5. The calculator displays the roots instantly.
  6. Click Show Step-by-Step Solution to see how the answer was found.

Quadratic Formula

The calculator uses the famous quadratic formula to find the roots.

x = (-b ± √(b² − 4ac)) / 2a

The symbol ± means there are usually two possible answers.

One answer uses the plus (+) sign and the other uses the minus (−) sign.

What is the Discriminant?

The discriminant tells us what kind of roots the quadratic equation has.

D = b² − 4ac

Discriminant Meaning
D > 0 Two different real roots
D = 0 One repeated real root
D < 0 Two complex roots

Example

Solve the equation:

x² + 6x + 8 = 0

Step 1

Identify the coefficients.

  • a = 1
  • b = 6
  • c = 8

Step 2

Find the discriminant.

D = 6² − 4 × 1 × 8

D = 36 − 32

D = 4

Step 3

Use the quadratic formula.

x = (-6 ± √4) / 2

x = (-6 ± 2) / 2

Step 4

x₁ = -2

x₂ = -4

Answer: The roots are -2 and -4.

Where Are Quadratic Equations Used?

Quadratic equations are used in many real-life situations.

  • Projectile motion in Physics
  • Engineering calculations
  • Architecture and bridge design
  • Computer graphics
  • Business profit calculations
  • Economics
  • Construction planning
  • Sports trajectory analysis
  • Satellite and space science
  • Machine learning and mathematics

Why Use Our Quadratic Equation Calculator?

  • Simple and easy to use
  • Free forever
  • No registration required
  • Works on mobile, tablet and desktop
  • Instant calculation
  • Accurate answers
  • Step-by-step explanations
  • Perfect for homework and exam preparation
  • Suitable for beginners and advanced learners
  • Available online anytime

Tips for Solving Quadratic Equations

  • Always check that a is not equal to zero.
  • Write the equation in standard form before solving.
  • Calculate the discriminant carefully.
  • Use brackets correctly while substituting values.
  • Verify your answers by putting them back into the original equation.