Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

(k + 1)^{2} = (k - 3) * (4 * k - 2) - 3 k^{2} + 16 k - 5 = 0 3 k^{2} - 16 k + 5 = 0 a = 3; b = - 16; c = 5 D = b^{2} - 4 a c = 1 6^{2} - 4 \cdot 3 \cdot 5 = 196 D > 0 k_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 6 \pm 1 9 6}{6} k_{1, 2} = \frac{1 6 \pm 1 4}{6} k_{1, 2} = 2.666667 \pm 2.333333 k_{1} = 5 k_{2} = 0.333333333 Factored form of the equation: 3 (k - 5) (k - 0.333333333) = 0

Solution in text:

-3k²+16k-5=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 196
D > 0 ... The equation has two distinct real roots

k₁ = 5
k₂ = 0.3333333

P = {5; 0.3333333}