Solve m_{2}=sqrt{5y}+sqrt{5(160-y)}

$$m _ { 2 } = \sqrt { 5 y } + \sqrt { 5 ( 160 - y ) }$$

Solve for m_2

$$m_{2}=\sqrt{800-5y}+\sqrt{5y}$$

$$y\geq 0\text{ and }y\leq 160$$

Solve for y

$$y=\frac{m_{2}\sqrt{1600-m_{2}^{2}}}{10}+80$$

$$y=-\frac{m_{2}\sqrt{1600-m_{2}^{2}}}{10}+80\text{, }m_{2}=20\sqrt{2}\text{ or }\left(m_{2}\leq 40\text{ and }m_{2}\geq 20\sqrt{2}\text{ and }m_{2}\sqrt{1600-m_{2}^{2}}\leq 800\right)$$