>>13014162(4x-17)/(5x+9) = (1/5) (4 - 121/(5x+9))
This is an integer iff 4 - 121/(5x+9) is an integer and multiple of 5
This is an integer iff 121/(5x+9) is an integer, ie. 5x+9 must be a factor of 121
121 is 11^2, so its factors are 1, 11, 121, -1, -11, -121
You can just check them all to get the possibilities x=-26, -4, -2
Plug them back in and you see they all work
