3/2x-1/x-5=1

Solution for 3/2x-1/x-5=1 equation:

D( x )

x = 0

x = 0

x = 0

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

(3/2)*x-(1/x)-5 = 1 // - 1

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

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

3/2*x^1-1*x^-1-6*x^0 = 0

(3/2*x^2-6*x^1-1*x^0)/(x^1) = 0 // * x^2

x^1*(3/2*x^2-6*x^1-1*x^0) = 0

x^1

(3/2)*x^2-6*x-1 = 0

(3/2)*x^2-6*x-1 = 0

DELTA = (-6)^2-(-1*4*(3/2))

DELTA = 42

DELTA > 0

x = (42^(1/2)+6)/(2*(3/2)) or x = (6-42^(1/2))/(2*(3/2))

x = (42^(1/2)+6)/3 or x = (6-42^(1/2))/3

x in { (6-42^(1/2))/3, (42^(1/2)+6)/3} 

x in { (6-42^(1/2))/3, (42^(1/2)+6)/3 }