Olympiad Geometry · Hard problem

Segments $\overline{AD}$ and $\overline{BE}$ intersect at $C$, which is the midpoint of $\overline{AD}$, and $\overline{AB} \parallel \overline{DE}$. If $AB = 2x + 3$, $DE = 5x - 9$, and $BC = x + 4$, find $BE$.