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Solve ax² + bx + c = 0 with discriminant, roots, vertex.
Solve quadratic equations ax² + bx + c = 0 instantly. Shows the discriminant, both real or complex roots, vertex, axis of symmetry, and a step-by-step explanation of the quadratic formula applied to your values.
The Quadratic Equation Solver instantly calculates roots, discriminants, vertices, and axes of symmetry for standard quadratic equations. It provides a complete step-by-step breakdown using the quadratic formula, supporting both real and complex roots without requiring software installation or account creation.
Good to know: This tool is focused exclusively on single quadratic equations, so users needing to solve systems of equations or perform advanced symbolic calculus will need a more comprehensive mathematics application.
Follow these steps to solve any quadratic equation and view detailed roots, discriminants, and vertex coordinates.
Identify your quadratic coefficients
Determine the values for a, b, and c from your equation in the standard form ax² + bx + c = 0.
Enter coefficients into the solver
Input your specific numerical values for a, b, and c into the designated fields within the tool.
Calculate the roots and discriminant
Click the solve button to instantly process the quadratic formula and determine if the roots are real or complex.
Review the step-by-step explanation
Examine the detailed breakdown of the formula application, including the vertex and axis of symmetry calculations.
Estimated time: PT1M
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x² + x + = 0
x₁
2
x₂
1
Discriminant
1
Vertex x
1.5
Vertex y
-0.25
D = b² − 4ac = (-3)² − 4·(1)·(2) = 1
→ Two distinct real roots
x = (−b ± √D) / 2a
