Quadratic Formula (Free)
Solve ax^2 + bx + c = 0 with real roots only.
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Full Quadratic Solver
Solve for complex roots, graph the parabola, and get step-by-step algebraic workings.
Frequently Asked Questions
What is the quadratic formula?
The quadratic formula x = (−b ± √(b² − 4ac)) / 2a gives the solutions to any quadratic equation ax² + bx + c = 0.
What is the discriminant?
The discriminant is b² − 4ac. If it is positive, there are two real roots. If it is zero, there is one repeated real root. If it is negative, the roots are complex.
When does a quadratic equation have no real solutions?
When the discriminant (b² − 4ac) is negative, the equation has no real solutions — only complex (imaginary) roots. The premium calculator handles complex roots.