How can I convert this equation: $$321^2 - 196^2 = 64625$$ to be in this form: $$X^2 - Y^2 + X = 64625$$
Whereas $X$ and $Y$ are Odds and $X > \sqrt{64625}$
I tried to find $X$ value by testing the values from 255 until 321 and I found $X=257$ and $Y=41$. So I would like to asking the mathematicians if there is any mathematical solution to find $X$ and $Y$ values?
Thanks for your help.
Times the equation by $4$, add 1 & complete the square \begin{eqnarray*} 4X^2+4X+1-4Y^2=4 \times 64625+1 \end{eqnarray*} which gives \begin{eqnarray*} (2X+1)^2-(2Y)^2=\color{red}{(2X-2Y+1)}\color{blue}{(2X+2Y+1)}=258501=\color{red}{433} \times \color{blue}{597}. \end{eqnarray*} etc ...