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Quadratic Equation Solver

Quadratic Equation Solver

Solve any quadratic equation ax² + bx + c = 0 and find real or complex roots with steps.

Enter Your Values
ax² + bx + c = 0
Results

Fill in your values above and click Calculate.

📐 Formula Used
x = (-b ± √(b²-4ac)) / 2anDiscriminant: b²-4ac > 0 → 2 real roots

Solve any quadratic equation ax² + bx + c = 0 and find real or complex roots with steps.

f(x) = ax² + bx + c sin(x) = opposite/hyp Mathematical Functions Visualization
Quadratic Equation Solver — CalculatorzKit

About the Quadratic Equation Solver

The Quadratic Equation Solver is a precise, free online math tool built for students, teachers, engineers, and professionals. It handles complex calculations instantly using floating-point arithmetic accurate to multiple decimal places — no installation, no account, no cost.

Part of our comprehensive Math Calculators collection, alongside the Percentage Calculator, Fraction Calculator, and Statistics Calculator.

📐 Formula & Methodology

x = (-b ± √(b²-4ac)) / 2anDiscriminant: b²-4ac > 0 → 2 real roots
The formula used by this calculator, verified against internationally recognized standards.

How to Use the Quadratic Equation Solver

Enter your values in the fields above and press Calculate. Results appear instantly with full precision. Adjust any input and results update automatically — no need to click Calculate again after the first run.

🎓 Understanding the Math

The formula displayed above follows standard mathematical conventions established in academic curricula worldwide. Use it to verify results manually, check your work, or deepen your understanding of the underlying mathematics. Our math calculator suite covers everything from basic arithmetic to advanced algebra, statistics, and geometry.

Who Uses This Calculator?

  • Students — homework help, exam prep, and understanding mathematical concepts
  • Teachers — generating examples, verifying solutions, and classroom demonstrations
  • Engineers and scientists — quick field calculations and design verification
  • Business professionals — percentage changes, ratios, growth rates, and margin calculations
  • Everyday users — splitting bills, calculating tips, figuring out discounts with the Discount Calculator

📐 Precision & Accuracy Notes

  • Results display up to 8 significant figures — trailing zeros are removed for readability
  • Very large or small results use scientific notation automatically
  • Double-check your inputs — small entry errors can significantly change results
  • Use the 📋 Copy button to paste results directly into documents or spreadsheets
  • Try our Scientific Calculator for advanced trigonometry, logarithms, and more

Frequently Asked Questions about the Quadratic Equation Solver

What does the discriminant tell you?

If b²-4ac > 0: two real roots. If = 0: one repeated root. If < 0: two complex (imaginary) roots.

What is the vertex of a parabola?

The vertex is the maximum or minimum point of the parabola at x = -b/(2a). The y-coordinate is c – b²/(4a).

Frequently Asked Questions

If b²-4ac > 0: two real roots. If = 0: one repeated root. If < 0: two complex (imaginary) roots.
The vertex is the maximum or minimum point of the parabola at x = -b/(2a). The y-coordinate is c - b²/(4a).