# These Are Not The Solutions You Are Looking For

Let all of the solutions of non-negative integers to the equation

$2x^{2}+x=3y^{2}+y$

be $$(x_{1},y_{1}),(x_{2},y_{2}),....$$, where $$x_{1}+y_{1}<x_{2}+y_{2}<.....$$. Find the value of $$\sum_{i=1}^{4}(x_{i}+y_{i})$$.

×