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令（1/x)=a 則a^2-a^3=36 a^2(1-a)=36=3×3×4=(-3)(-3)(4) 則a=-3 x=-1/3

The first thing I did was set (1/x)=-u, so our equation becomes u^3+u^2 = 36. I hope it's obvious why that substitution gives us a simpler equation. I can make a guess that the result for u is an integer. If that is wrong, I need another method. But it's sort of hard to add together two fractions and get an integer. Now we make an obvious guess, u=3 -- among integers, u 36. Quickly we see that 1/x=-3 makes x=(-1/3). Any other solutions would have to be complex numbers.

x = -1/3

Wow. Absolutely no explanations as to why you are doing what you do. Its as though from the beginning that three to some power would yield the answers.