Quadratic Equation Calculator
Solve equations of the form ax² + bx + c = 0 using the quadratic formula.
How to Use
- Enter values for a, b, and c.
- Ensure a ≠ 0.
- Click Solve Equation.
- View the roots and discriminant below.
Solve Any Equation Instantly
Looking for a fast and accurate way to solve quadratic equations? Our Quadratic Equation Calculator helps you instantly find the roots of any equation in the form:
ax² + bx + c = 0
Simply enter your values, click Solve Equation, and get immediate results including the discriminant and both real or complex solutions.
What Is a Quadratic Equation?
A quadratic equation is a second-degree polynomial equation written as:
ax² + bx + c = 0
Where:
- a ≠ 0
- b and c are constants
- x represents the unknown variable
Quadratic equations are widely used in:
- Physics (motion and trajectories)
- Engineering calculations
- Finance and business models
- Mathematics education
How This Quadratic Calculator Works
This calculator uses the quadratic formula:
x = (-b ± √(b² – 4ac)) / (2a)
Once you enter values for a, b, and c, the tool will:
✔ Calculate the discriminant (D = b² – 4ac)
✔ Determine the type of roots
✔ Display the final solutions instantly
Understanding the Discriminant
The discriminant (D) tells you what type of solutions your equation has:
- D > 0 → Two real and distinct roots
- D = 0 → One real root (repeated)
- D < 0 → Two complex (imaginary) roots
This calculator automatically handles all three cases.
Step-by-Step: How to Use the Calculator
- Enter the value of a
- Enter the value of b
- Enter the value of c
- Click Solve Equation
- View your results instantly
⚠️ Note: The value of a cannot be 0, otherwise the equation is not quadratic.
Example Calculation
Solve:
x² – 3x + 2 = 0
- a = 1
- b = -3
- c = 2
Using the formula, the solutions are:
x₁ = 2
x₂ = 1
Why Use Our Quadratic Equation Calculator?
✔ 100% Free and instant results
✔ Works on all devices (mobile, tablet, desktop)
✔ Handles real and complex roots
✔ No downloads or sign-ups required
✔ Accurate mathematical calculations
Real-World Applications of Quadratic Equations
Quadratic equations are more useful than you might think. They are used in:
- Projectile motion (e.g., calculating the path of a ball)
- Profit optimization in business
- Engineering design calculations
- Computer graphics and simulations
Frequently Asked Questions (FAQs)
What is the easiest way to solve a quadratic equation?
The easiest method is using the quadratic formula, which this calculator applies automatically.
Can this calculator solve complex roots?
Yes. If the discriminant is negative, the calculator provides solutions in complex number form (a ± bi).
What happens if a = 0?
If a = 0, the equation becomes linear, not quadratic, and the calculator will show an error.
Is this calculator accurate?
Yes, it uses precise mathematical formulas to deliver accurate results instantly.
Start Solving Quadratic Equations Now
Use the calculator above to solve any quadratic equation in seconds. Whether you’re a student, teacher, or professional, this tool makes solving equations quick and effortless.