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D( x )
x = 0
x = 0
x = 0
x in (-oo:0) U (0:+oo)
(1/2)*x+(1/3)*x+1/x = 18 // - 18
(1/2)*x+(1/3)*x+1/x-18 = 0
5/6*x^1+1*x^-1-18*x^0 = 0
(5/6*x^2-18*x^1+1*x^0)/(x^1) = 0 // * x^2
x^1*(5/6*x^2-18*x^1+1*x^0) = 0
x^1
(5/6)*x^2-18*x+1 = 0
(5/6)*x^2-18*x+1 = 0
DELTA = (-18)^2-(1*4*(5/6))
DELTA = 962/3
DELTA > 0
x = ((962/3)^(1/2)+18)/(2*(5/6)) or x = (18-(962/3)^(1/2))/(2*(5/6))
x = 3/5*((962/3)^(1/2)+18) or x = 3/5*(18-(962/3)^(1/2))
x in { 3/5*(18-(962/3)^(1/2)), 3/5*((962/3)^(1/2)+18)}
x in { 3/5*(18-(962/3)^(1/2)), 3/5*((962/3)^(1/2)+18) }
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