$$ \begin{aligned} & \sqrt{5}\, x=\sqrt{3}\, x+32 \\ \Leftrightarrow & \; \sqrt{5}\, x -\sqrt{3}\, x=32 \\ \Leftrightarrow & \; ( \sqrt{5}\, x -\sqrt{3} ) \, x=32 \\ \Leftrightarrow & \; x=\frac{32}{\sqrt{5}\, -\sqrt{3}} \\ \Leftrightarrow & \; x = \frac{32\cdot (\sqrt{5}\, +\sqrt{3})} {(\sqrt{5}\, -\sqrt{3}).(\sqrt{5}\, +\sqrt{3})} \\ \Leftrightarrow & \; x=\frac{32\cdot (\sqrt{5}\, +\sqrt{3})} {5-3} \\ \Leftrightarrow & \; x = 16 \cdot (\sqrt{5}\, +\sqrt{3}) \end{aligned} $$