🍋 Math Tools
Equation Solver
Solve linear and quadratic equations step by step
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About Equation Solver
Solve linear equations (ax + b = 0) and quadratic equations (ax² + bx + c = 0) with step-by-step solutions. See the discriminant, roots, and vertex for quadratic equations.
How It Works
For linear equations, the tool solves x = -b/a. For quadratic equations, it calculates the discriminant (b²-4ac) and applies the quadratic formula. Complex roots are shown when the discriminant is negative.
Step by Step
- 1 Select equation type: linear (ax + b = 0) or quadratic (ax² + bx + c = 0)
- 2 Enter coefficients (e.g., 2 -3 for 2x - 3 = 0)
- 3 Click Solve to see the step-by-step solution
Tips
- For quadratic equations, a positive discriminant means two real roots
- A discriminant of zero means one repeated root (the vertex touches the x-axis)
- A negative discriminant means complex conjugate roots
- The vertex of a parabola is at x = -b/(2a)
Frequently Asked Questions
What is the quadratic formula?
x = (-b ± √(b²-4ac)) / (2a). It gives the two solutions (roots) of any quadratic equation ax² + bx + c = 0.
What does the discriminant tell you?
The discriminant (b²-4ac) determines the nature of roots: positive = two distinct real roots, zero = one repeated root, negative = two complex conjugate roots.