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 \(BC = y = {105 \over 4}\).