How do I use the Quadratic Formula Calculator?
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Quadratic Formula Calculator
Solve quadratic equations ax² + bx + c = 0. Enter your values, review the formula, and use the worked result as a quick check for everyday planning.
Quadratic Formula Calculator
Solve quadratic equations ax² + bx + c = 0.
Any numeric value (not zero)
Any numeric value
Any numeric value
Results
Discriminant
1
x₁
2
x₂
1
Formula: x = (-b ± √(b² - 4ac)) / 2a
Quadratic Formula Solver
Solve any quadratic equation of the form ax² + bx + c = 0 using the quadratic formula. The calculator computes the discriminant and both real roots (solutions). If the discriminant is negative, it reports no real solutions.
Formula
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant (b² − 4ac) determines how many real solutions exist: positive = two solutions, zero = one solution, negative = no real solutions.
Worked example
a = 1, b = −3, c = 2: discriminant = 9 − 8 = 1 → x₁ = (3 + 1)/2 = 2, x₂ = (3 − 1)/2 = 1.
Practical guidance
What the discriminant tells you
When the discriminant is positive, the parabola crosses the x-axis at two points (two real solutions). When zero, it touches at one point (one double root). When negative, the parabola does not cross the x-axis (no real solutions).
Coefficient a must not be zero
If a = 0, the equation is linear (bx + c = 0), not quadratic. The quadratic formula involves division by 2a, which fails when a = 0. For linear equations, the solution is simply x = −c/b.
Frequently asked questions
What formula does this calculator use?
x = (-b ± √(b² - 4ac)) / 2a
Can I use decimal values?
Yes. Decimal inputs are supported for most calculators. Integer-based tools use rounded integer values where appropriate.
Is this calculator free?
Yes. CalcuNimble calculators are free and optimized for fast everyday use.