Quadratic Formula Calculator
Solve quadratic equations in the form ax² + bx + c = 0 using the quadratic formula, with real or complex roots and full calculation steps.
ax² + bx + c = 0
Results
Root x₁
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Root x₂
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Discriminant
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Root type
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Equation
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Vertex
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Axis of symmetry
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Calculation details
Use this Quadratic Formula Calculator to solve equations in the form ax² + bx + c = 0. It calculates the roots, discriminant, vertex, and axis of symmetry.
Calculation Method
Quadratic formula:
x = (−b ± √(b² − 4ac)) ÷ 2a
Discriminant:
D = b² − 4ac
- D > 0: two real roots
- D = 0: one repeated real root
- D < 0: two complex roots
The x-coordinate of the vertex and axis of symmetry is:
x = −b ÷ 2a
Example
Solve:
2x² + 5x − 3 = 0
First calculate the discriminant:
D = 5² − 4(2)(−3) = 49
Then:
x = (−5 ± √49) ÷ 4
The roots are:
x = 0.5 and x = −3
Important Note
The coefficient a cannot be zero. If a = 0, the equation is linear rather than quadratic. Long decimal results may be rounded for display.