Quadratic equation calculator

Quadratic equation has the basic form:

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

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

54 = n (n - 3) / 2 - 0.5 n^{2} + 1.5 n + 54 = 0 0.5 n^{2} - 1.5 n - 54 = 0 a = 0.5; b = - 1.5; c = - 54 D = b^{2} - 4 a c = 1 . 5^{2} - 4 \cdot 0.5 \cdot (- 54) = 110.25 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 . 5 \pm 1 1 0 . 2 5}{1} n_{1, 2} = 1.5 \pm 10.5 n_{1} = 12 n_{2} = - 9 Factored form of the equation: 0.5 (n - 12) (n + 9) = 0

Solution in text:

-0.5n²+1.5n+54=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 110.25
D > 0 ... The equation has two distinct real roots

n₁ = 12
n₂ = -9

P = {12; -9}