Scientific Quadratic Equation Solver
Solve any quadratic equation with step-by-step solutions and interactive graph visualization
Enter Coefficients
Solution & Graph
Equation: 1x² - 3x + 2 = 0
Step 1: Identify coefficients: a = 1, b = -3, c = 2
Step 2: Calculate discriminant: D = b² - 4ac = (-3)² - 4*1*2 = 9 - 8 = 1
Step 3: Since D > 0, there are two real solutions
Step 4: Apply quadratic formula: x = [-b ± √D] / (2a)
Step 5: Calculate solutions:
x₁ = [3 + √1] / 2 = 4/2 = 2
x₂ = [3 - √1] / 2 = 2/2 = 1
x₁ = [3 + √1] / 2 = 4/2 = 2
x₂ = [3 - √1] / 2 = 2/2 = 1
Discriminant (D)
1
Root 1 (x₁)
2
Root 2 (x₂)
1
Frequently Asked Questions
What is a quadratic equation?
A quadratic equation is a second-degree polynomial equation in a single variable x, with the form ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.
What is the quadratic formula?
The quadratic formula is x = [-b ± √(b² - 4ac)] / (2a). It provides the solutions to any quadratic equation.
What does the discriminant tell us?
The discriminant (D = b² - 4ac) determines the nature of the roots: If D > 0, two distinct real roots; D = 0, one real root; D < 0, two complex roots.
How do I use this calculator?
Enter the coefficients a, b, and c of your quadratic equation (ax² + bx + c = 0) and click 'Solve'. The solution with steps and graph will be displayed.