Quadratic Formula Calculator | Solve Real & Complex Roots
Solve quadratic equations ax²+bx+c=0 step-by-step. Get real and complex roots, discriminant analysis, vertex details, and parabola graphing values.
ax² + bx + c = 0
Equation roots (x)
x₁ = 3
x₂ = 2
x₂ = 2
SolvedD = 1
Root Type Verdict
two real Roots
Parabolic Geometric Specifications
Vertex (h, k)(2.5, -0.25)
Axis of Symmetryx = 2.5000
Y-Intercept(0, 6)
Openingupward
Continuous Parabolic Curve Representation
Step-by-step discriminant analysis solver
Identify Coefficients
a, b, c → a = 1, b = -5, c = 6
Calculate Discriminant (D)
D = b² − 4ac → D = (-5)² − 4(1)(6) = 25 − 24 = 1
Evaluate Roots (D > 0)
x = (-b ± √D) / 2a → x = (-(-5) ± √1) / (2 * 1) = (5 ± 1.0000) / 2
Final Roots Resolution
x₁, x₂ → x₁ = 3.0000, x₂ = 2.0000