Quadratic Formula Calculator

Struggling with quadratic equations? Our Quadratic Formula Calculator makes it simple. Just type in your numbers and get quick answers.

quadratic formula calculator

Enter Information:
X2
+
X
+
= 0
3x2 + 5x + 2

RESULTS

Fill the calculator form and click on Calculate button to get result here
Detail
The coefficients of quadratic equation are:
--
Discriminant:
--
Roots
--
Answer
--

How to Use the Calculator:

  1. Type your values into the boxes labeled a, b, and c.

  2. Click the Calculate button.

  3. The calculator shows you each step:

    • It flips the sign of b

    • Works out what’s under the square root (that’s the discriminant)

    • Then divides everything by 2a

  4. You’ll get two answers for x—or just one if the equation has a double root.

It even explains each part so you can follow along and learn as you go.

What Is a Quadratic Equation?

A quadratic equation is a math expression that looks like this:

ax² + bx + c = 0

Here’s what the letters mean:

  • a is the number in front of x²

  • b is the number in front of x

  • c is just a regular number, called the constant

These equations often show up in algebra and even in real life—like figuring out how things move or curve.

Now you can Solve for the length of the sides of a right triangle using our Pythagorean Theorem Calculator.

The Formula That Does the Heavy Lifting

To solve a quadratic equation, we use this classic formula:

x = (-b ± √(b² – 4ac)) / 2a

It sounds like a lot, but the calculator handles all the tricky parts for you.

Key Parts of the Formula

Element Description
a Number in front of x²
b Number in front of x
c The constant term
± Means you get two possible answers
√(b² – 4ac) The discriminant—it tells you what kind of answers to expect

What Does the Discriminant Tell You?

The discriminant is the part under the square root:

D = b² – 4ac

This little number tells you what kind of answers you’ll get:

  • If it’s positive, there are two real solutions
  • If it’s zero, you get one real solution (a repeated root)
  • If it’s negative, you get two complex solutions (don’t worry, the calculator explains those too)

Knowing this upfront helps you understand how your equation will look when graphed.

What Kind of Solutions Will You Get?

Discriminant (b² – 4ac) Type of Solutions Example
Positive Two real solutions x₁ = (-5 + √49)/2, x₂ = (-5 – √49)/2
Zero One real repeated root x = (-3 + √0)/2
Negative Two complex solutions x₁ = (-2 + √-8)/2, x₂ = (-2 – √-8)/2

Try It With These Examples

Example 1: Solve 2x² + 5x – 3 = 0

  • a = 2, b = 5, c = -3
  • x = (-5 ± √(25 + 24)) / 4
  • x = (-5 ± √49) / 4

Example 2: Solve x² + 4x + 4 = 0

  • a = 1, b = 4, c = 4
  • x = (-4 ± √(16 – 16)) / 2
  • x = -2 (repeated root)

Recap

Whether you’re a student trying to finish your homework or just brushing up on algebra, the Quadratic Formula Calculator is here to help. It does more than just give you the answer, it walks you through each step, shows you a visual graph, and helps you actually understand what you’re solving.

Related Calculators:

 

Leave a Comment