Math
Equation Solver
Solve quadratic equations and systems of linear equations
Solutionx₁ = 2.0000
x₂ = 1.0000 View results
Real-time Results
System of Equations
1x² + (-3)x + (2) = 0
Coefficient Determinant D
1.0000
Solution Type
Two distinct real roots
Solution
x₁ = 2.0000
x₂ = 1.0000
Solution to the equation
Solution Steps
Step-by-step solution process
| Item | Value |
|---|---|
| Step 1: Identify the quadratic equation Identify the standard form of the quadratic equation to solve. | 1x² + (-3)x + (2) = 0 |
| Step 2: Calculate discriminant Δ = b² - 4ac Calculate the discriminant to determine the nature of roots. | Δ = (-3)² - 4 × (1) × (2) = 9 - 8 = 1 |
| Step 3: Calculate two distinct real roots Since Δ > 0, the equation has two distinct real roots. | x₁ = (-(-3) + √1) / (2 × 1) = (3 + 1.0000) / 2 = 2.0000 x₂ = (-(-3) - √1) / (2 × 1) = (3 - 1.0000) / 2 = 1.0000 |
Supported inputs
| Input | Description |
|---|---|
| Equation Type | Select the equation type to solve Quadratic Equation · Linear System |
| Coefficient a (x²) | Coefficient a |
| Coefficient b (x) | Coefficient b |
| Coefficient c (constant) | Coefficient c |
| Equation 1: a₁ (x coefficient) | Coefficient a₁ |
| Equation 1: b₁ (y coefficient) | Coefficient b₁ |
| Equation 1: c₁ (constant) | Constant term c₁ |
| Equation 2: a₂ (x coefficient) | Coefficient a₂ |
| Equation 2: b₂ (y coefficient) | Coefficient b₂ |
| Equation 2: c₂ (constant) | Constant term c₂ |
| Decimal Places | Number of decimal places |
Formula
Quadratic (ax² + bx + c = 0): Discriminant Δ = b² - 4ac Roots: x = (-b ± √Δ) / 2a Linear System: D = a1*b2 - a2*b1 Dx = c1*b2 - c2*b1 Dy = a1*c2 - a2*c1 x = Dx/D, y = Dy/D
Related Calculators
More calculators selected by category and topic.
Complementary Tools
Related Tags: