1. The problem statement, all variables and given/known data I am a hobbyist looking for solutions to ax^2 + bx - cy^2 - dy = 0 where all variables are integers and are non-zero. Is there a method of doing this effectively? 2. Relevant equations 3. The attempt at a solution I can look at the numbers produced by ax^2 + bx vs cy^2 + dy and see that they have a relationship: what I mean is if I manually find a pair of close numbers, difference = d, I find the next set of values is d+2 apart, then d + 4 and so on. So it looks as though there should be a method in algebraic terms for doing this.