Quadratic Equation Solver

What is the Quadratic Equation Solver?

Solve ax² + bx + c = 0 with the quadratic formula, including complex roots. The quadratic formula solves any equation of the form ax² + bx + c = 0, including those with complex roots.

How to use the Quadratic Equation Solver

1. Enter your a, your b, your c.
2. Results update automatically as you type; you can also press Calculate.
3. Read the output: roots, discriminant (b² − 4ac), vertex.
4. Use the 📊 chart to see the result visually, then copy or share it.

Formula and method

Worked example

With a = 1, b = -3, c = -10, the Quadratic Equation Solver returns roots: x₁ = 5, x₂ = -2; discriminant (b² − 4ac): 49; vertex: (1.5, -12.25).

Where the Quadratic Equation Solver helps in real life

An algebra student needs the roots of 2x² − 7x + 3 = 0. The solver gives x = 3 and x = 0.5 and shows the discriminant.

A physics student models a ball thrown upward and needs the time it hits the ground. Solving the quadratic gives the positive root, which is the landing time.

Common mistakes to avoid

• Entering a = 0, which makes the equation linear.
• Dropping the negative sign on b.
• Misreading a negative discriminant as no solution at all.
• Rounding the square root of the discriminant too early.

💡 Practical tip: A negative discriminant means the roots are complex, so the graph never crosses the x-axis.

Tips for better results

• Rearrange the equation into ax² + bx + c = 0 first.
• Check the discriminant to know how many real roots to expect.
• Substitute the roots back in to verify them.

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