Just use all the ways -36 can be written as the
product of two integer factors:

If k is a NON-NEGATIVE integer, then
these 5 are the only ways

(y+1)(y-36) = y²-35x-36   k=35
(y+2)(y-18) = y²-16x-36   k=16
(y+3)(y-12) = y²-9x-36    k=9
 (y+4)(y-9) = y²-5x-36    k=5
 (y+6)(y-6) = y²-0x-36    k=0

If k is a NEGATIVE integer, then
these 4 are the only ways

(y-1)(y+36) = y²+35x-36   k=-35
(y-2)(y+18) = y²+16x-36   k=-16
(y-3)(y+12) = y²+9x-36    k=-9
 (y-4)(y+9) = y²+5x-36    k=-5

Edwin
 

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