x*(30/x)=(x-1)((30/x)+1)

Solution for x*(30/x)=(x-1)((30/x)+1) equation:

D( x )

x = 0

x = 0

x = 0

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

(30/x)*x = (x-1)*(30/x+1) // - (x-1)*(30/x+1)

(30/x)*x-((x-1)*(30/x+1)) = 0

30-1*(x-1)*(30*x^-1+1) = 0

30-1*(x-1)*(30*x^-1+1) = 0

30*x^-1-x+1 = 0

30*x^-1-x+1 = 0

30*x^-1-1*x^1+1*x^0 = 0

(1*x^1-1*x^2+30*x^0)/(x^1) = 0 // * x^2

x^1*(1*x^1-1*x^2+30*x^0) = 0

x^1

x-x^2+30 = 0

x-x^2+30 = 0

DELTA = 1^2-(-1*4*30)

DELTA = 121

DELTA > 0

x = (121^(1/2)-1)/(-1*2) or x = (-121^(1/2)-1)/(-1*2)

x = -5 or x = 6

x in { -5, 6} 

(x+5)*(x-6) = 0

(x+5)*(x-6) = 0

( x+5 )

x+5 = 0 // - 5

x = -5

( x-6 )

x-6 = 0 // + 6

x = 6

x in { -5, 6 }