Quadratic Equation Calculator
Solve quadratic equations of the form ax² + bx + c = 0. Get real and complex roots with step-by-step solution using the quadratic formula.
Published by:
isCalculator Editorial Team
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How to Use the Quadratic Equation Calculator
This tool solves equations of the form ax² + bx + c = 0 using the quadratic formula. Follow these steps:
- Enter coefficients a, b, and c in the input fields. Use decimal numbers (e.g., 1, -3.5) as needed.
- Ensure a is non-zero — the calculator will show an error if a = 0 (the equation would be linear).
- Click "Solve" to compute the roots.
- View the discriminant (Δ = b² - 4ac) which tells you the root type:
- Δ > 0 → two distinct real roots
- Δ = 0 → one real double root
- Δ < 0 → two complex roots (displayed as a ± bi)
- Results show roots rounded to 6 decimal places, plus a step-by-step breakdown of the calculation.
Tip: All inputs accept integers, decimals, or negative numbers. No units needed — just pure coefficients.
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Frequently Asked Questions
The quadratic formula solves equations of the form ax²+bx+c=0: x = [-b ± √(b²-4ac)] / (2a).
The discriminant (Δ = b²-4ac) determines the nature of roots: if Δ>0, two distinct real roots; if Δ=0, one real double root; if Δ<0, two complex roots.
Yes, you can enter any real numbers for a, b, and c. a must be non-zero.
