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:

(6 n + 1) (4 n - 1) = 3 n^{2} 21 n^{2} - 2 n - 1 = 0 a = 21; b = - 2; c = - 1 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 21 \cdot (- 1) = 88 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 \pm 8 8}{4 2} = \frac{2 \pm 2 2 2}{4 2} n_{1, 2} = 0.047619 \pm 0.223353 n_{1} = 0.270972179 n_{2} = - 0.175734084 Factored form of the equation: 21 (n - 0.270972179) (n + 0.175734084) = 0

Solution in text:

21n²-2n-1=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 88
D > 0 ... The equation has two distinct real roots

n₁ = 0.2709722
n₂ = -0.1757341

P = {0.2709722; -0.1757341}