$
\eqalign{
  & \frac{1}
{{\sqrt 3 }} = \frac{{50 - x}}
{x}  \cr
  & x = \left( {50 - x} \right) \cdot \sqrt 3   \cr
  & x = 50\sqrt 3  - x\sqrt 3   \cr
  & x + x\sqrt 3  = 50\sqrt 3   \cr
  & x\left( {1 + \sqrt 3 } \right) = 50\sqrt 3   \cr
  & x = \frac{{50\sqrt 3 }}
{{1 + \sqrt 3 }} = 75 - 25\sqrt 3  \cr}
$