Recursive equations for quadratic diophantine equations.

How do I determine the recursive equations for deriving integer solutions to quadratic Diophantine equations. Say I have a Diophantine equation. e.g.

$5{x}^{2}-3x+3{y}^{2}+2y=0$

How do I determine a recursive equation so that with one integer solution I can determine the other integer solutions.

How do I determine the recursive equations for deriving integer solutions to quadratic Diophantine equations. Say I have a Diophantine equation. e.g.

How do I determine a recursive equation so that with one integer solution I can determine the other integer solutions.