Like the Programm for (multiple + factor)^2 - (factor)^2 (expressions from (approx_root - n )^2 + multiple * (approx_root - n) + rest = Z )
the Formular should be generalized to get integer result for every giveen number. As you can chose your appropriate n, it is trivial that there is at least one (mostly two).
But even with a rational result this can be a good base for further developement.
As such, calculating rsa300 in this way, the result were to rational numbers p and q, whose sum p+q is integer, and whose product is rsa300.e