Geometry

y / 14 = (y + 15) / 22

By similarity, ${30 \over 30 + x} = {y \over y + 15} = {14 \over 22} = {7 \over 11}$, and you want to find $y$. Using ${ y \over y + 15} = {7 \over 11}$, we get $11y = 7y + 105$, so $4y = 105$, so $BC = y = {105 \over 4}$.