Quadratic Equation Solver

Solve quadratic algebraic equations of the form `ax² + bx + c = 0`. Calculates real or complex imaginary roots ($x_1$, $x_2$), discriminant ($Delta = b^2 - 4ac$), and vertex coordinates with step-by-step work.

Why Use This Tool?

• Algebra Homework: Verify solutions for quadratic equations with real or complex numbers.
• Physics Trajectory Math: Calculate projectile motion parabolic arcs and impact times.
• Discriminant Analysis: Determine whether an equation has 2 distinct real roots, 1 repeated real root, or 2 complex imaginary roots.

How to Use

1. Enter coefficients $a$, $b$, and $c$ (e.g. $a = 1, b = -5, c = 6$).
2. Click Solve Equation.
3. View Discriminant ($Delta$), Roots ($x_1, x_2$), Vertex $(h, k)$, and step-by-step formula derivations.

Real Working Example

Input:

Equation: 1x² - 5x + 6 = 0 (a=1, b=-5, c=6)

Output Result:

Discriminant (b²-4ac): 1 (Positive) | Roots: x1 = 3.0, x2 = 2.0 | Vertex: (2.5, -0.25)

Important Technical Details & Formulas

• Quadratic Formula Standard: `x = (-b ± √(b² - 4ac)) / (2a)`.
• Complex Imaginary Number Support: Handles negative discriminants using $i = sqrt{-1}$ (e.g. $2 pm 3i$).
• Client-Side Engine: Fast local execution in browser memory.

Related Mathematics & Financial Tools

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