3/2x-5/x-5=4/x

Solution for 3/2x-5/x-5=4/x equation:

D( x )

x = 0

x = 0

x = 0

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

(3/2)*x-(5/x)-5 = 4/x // - 4/x

(3/2)*x-(5/x)-(4/x)-5 = 0

(3/2)*x-5*x^-1-4*x^-1-5 = 0

3/2*x^1-9*x^-1-5*x^0 = 0

(3/2*x^2-5*x^1-9*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2-5*x^1-9*x^0) = 0

x^1

(3/2)*x^2-5*x-9 = 0

(3/2)*x^2-5*x-9 = 0

DELTA = (-5)^2-(-9*4*(3/2))

DELTA = 79

DELTA > 0

x = (79^(1/2)+5)/(2*(3/2)) or x = (5-79^(1/2))/(2*(3/2))

x = (79^(1/2)+5)/3 or x = (5-79^(1/2))/3

x in { (5-79^(1/2))/3, (79^(1/2)+5)/3} 

x in { (5-79^(1/2))/3, (79^(1/2)+5)/3 }