let $\arctan2(x,y)$ be the quadrant adjusted arc tangent of point $(x,y)$
$\theta = \arctan2(x,400)$
$\beta = \arctan2(x,225)$
$\alpha(x) = \theta-\beta = \arctan2(x,400)-\arctan2(x,225)$
$\dfrac {d \alpha}{dx}= \dfrac{225}{x^2+50625}-\dfrac{400}{x^2+160000}$
Now solve
$\dfrac {d \alpha}{dx} = 0$ for $x$