I should mention that there is a more mathematical way to determine a good value for x.

Since our goal is to make cube_root(90x) an integer, we need 90x to be equal to the CUBE of some integer.
In other words, we want 90x = k³ (where k is some integer)

The prime factorization of 90 = (2)(3)(3)(5)
So, if we add to the above prime factorization two more 2's, one more 3 and two more 5's, we get: (2)(2)(2)(3)(3)(3)(5)(5)(5)

Notice that (2)(2)(2)(3)(3)(3)(5)(5)(5)(5) is the CUBE of an integer.
We know this because: (2)(2)(2)(3)(3)(3)(5)(5)(5) = [(2)(3)(5)] * [(2)(3)(5)] * [(2)(3)(5)] = [(2)(3)(5)]³

Notice that by adding two more 2's, one more 3 and two more 5's to the prime factorization, we are basically multiplying by 300 (since (2)(2)(3)(5)(5) = 300