5/4x-24=-8/x-6

Solution for 5/4x-24=-8/x-6 equation:

D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

(5/4)*x-24 = -8/x-6 // + -8/x-6

(5/4)*x-(-8/x)-24+6 = 0

(5/4)*x+8*x^-1-24+6 = 0

5/4*x^1+8*x^-1-18*x^0 = 0

(5/4*x^2-18*x^1+8*x^0)/(x^1) = 0 // * x^2

x^1*(5/4*x^2-18*x^1+8*x^0) = 0

x^1

(5/4)*x^2-18*x+8 = 0

(5/4)*x^2-18*x+8 = 0

DELTA = (-18)^2-(4*8*(5/4))

DELTA = 284

DELTA > 0

x = (284^(1/2)+18)/(2*(5/4)) or x = (18-284^(1/2))/(2*(5/4))

x = 2/5*(2*71^(1/2)+18) or x = 2/5*(18-2*71^(1/2))

x in { 2/5*(18-2*71^(1/2)), 2/5*(2*71^(1/2)+18)} 

x in { 2/5*(18-2*71^(1/2)), 2/5*(2*71^(1/2)+18) }