How to determine x which is giving integer value

Question

So I have numbers which are giving division perfectly when x value is correct.

 

(30+77x) / (77-x)                           , if x is 18 division value is integer.  How the heck I can check this whitout trying every

 

number from 1 to n??

Answer 1

I invite you to rewrite this question more clearly. 

If the question comes from a class/textbook, state it exactly (including all context).