Quadratic Formula
ax² + bx + c = 0
x = (−b ± √(b² − 4ac)) / 2a
Discriminant Δ = b² − 4ac:
Δ > 0 → two distinct real roots
Δ = 0 → one repeated real root
Δ < 0 → two complex conjugate roots
Quadratic Equation Calculator
Solve any quadratic equation in the form ax² + bx + c = 0. Enter the coefficients a, b, and c to find all real and complex roots using the quadratic formula, with step-by-step solution shown.
Solve ax² + bx + c = 0
Frequently Asked Questions
What is the discriminant?
The discriminant (b² − 4ac) determines the nature of the roots. If positive, there are two real solutions; if zero, one repeated solution (the parabola touches the x-axis at one point); if negative, two complex solutions (parabola doesn't cross the x-axis).
What if a = 0?
If a = 0, the equation becomes linear (bx + c = 0), not quadratic. The quadratic formula requires a ≠ 0. A linear equation has exactly one solution: x = −c/b.
About the Quadratic Equation Calculator
This free quadratic equation calculator helps you get accurate results instantly without needing to work through the math manually. Whether you need a quick estimate or a precise figure, having a reliable tool on hand saves time and reduces errors compared to manual calculation.
How to Use This Calculator
- Enter your values in the input fields above. Each field is labeled to guide you.
- Double-check your inputs — results are only as accurate as the numbers you enter.
- Click the Calculate button to see your result instantly.
- Use the result for your planning, budgeting, or decision-making.
Why Accurate Calculations Matter
Small errors in math calculations can compound into significant problems. A 1% miscalculation in a budget or measurement can translate to hundreds or thousands of dollars in wasted resources, or result in having to redo work entirely. This calculator uses the standard formulas and methods to give you reliable results you can trust.
Tips for Getting the Best Results
- Use consistent units throughout (all in feet, all in dollars, etc.)
- For estimates, add a 10% buffer to account for real-world variables
- Save your result by taking a screenshot or writing it down before closing the page
- For decisions involving significant money or safety, verify results with a qualified professional
Frequently Asked Questions
Is this calculator free? Yes — completely free with no account, login, or payment required. Use it as many times as you need.
How accurate are the results? This calculator uses the standard formulas for quadratic equation calculations. Results are accurate for typical use cases. For specialized or high-stakes applications, consult a professional.
Does it work on mobile? Yes. This calculator is fully responsive and works on smartphones, tablets, and desktops.