Method
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant determines whether two real, one repeated, or two complex roots exist.
Math worksheet
Quadratic Formula Calculator
Solve ax² + bx + c = 0, classify the discriminant, and show real or complex roots, vertex and axis of symmetry.
The calculation runs locally. Exact-integer tools avoid floating point; decimal and transcendental tools report rounding limits.
Method and verification guide
How the Quadratic Formula Calculator works
x = (−b ± √(b² − 4ac)) ÷ 2a. The discriminant determines whether two real, one repeated, or two complex roots exist. The calculator keeps the intermediate values visible so you can reproduce the answer independently.
Interpret the result
Roots are x-intercepts when real. The vertex lies at x = −b/(2a).
Check the assumptions
Coefficient a must be nonzero; otherwise the equation is linear rather than quadratic.
Local calculation
Everything runs in this browser. Inputs are not sent to an external calculator.
Rounding
Displayed values may be rounded for readability while calculations use full floating-point precision unless the tool explicitly uses exact integers.
Scope
Coefficient a must be nonzero; otherwise the equation is linear rather than quadratic.
Simple by design
Three steps to a clearer number.
Enter your details
Use realistic values in each field. You can change them anytime.
Calculate instantly
The formula runs locally, so there is no account or waiting time.
Use the result
Treat the answer as a practical estimate for your next decision.