Solve frac{m_{1}x_{1}+2m_{2}x_{2}}{m_{1}+2m_{2}}=34

$$\frac { m _ { 1 } x _ { 1 } + 2 m _ { 2 } x _ { 2 } } { m _ { 1 } + 2 m _ { 2 } } = 34$$

Solve for m_2 (complex solution)

$$\left\{\begin{matrix}m_{2}=-\frac{m_{1}\left(x_{1}-34\right)}{2\left(x_{2}-34\right)}\text{, }&\left(x_{1}=34\text{ or }x_{2}\neq x_{1}\right)\text{ and }m_{1}\neq 0\text{ and }x_{2}\neq 34\\m_{2}\neq 0\text{, }&m_{1}=0\text{ and }x_{2}=34\\m_{2}\neq -\frac{m_{1}}{2}\text{, }&x_{1}=34\text{ and }x_{2}=34\end{matrix}\right.$$

Solve for m_1

$$\left\{\begin{matrix}m_{1}=-\frac{2m_{2}\left(x_{2}-34\right)}{x_{1}-34}\text{, }&m_{2}\neq 0\text{ and }x_{1}\neq x_{2}\text{ and }x_{1}\neq 34\\m_{1}\neq -2m_{2}\text{, }&\left(m_{2}=0\text{ or }x_{2}=34\right)\text{ and }x_{1}=34\end{matrix}\right.$$

Solve for m_2

$$\left\{\begin{matrix}m_{2}=-\frac{m_{1}\left(x_{1}-34\right)}{2\left(x_{2}-34\right)}\text{, }&m_{1}\neq 0\text{ and }x_{2}\neq 34\text{ and }x_{1}\neq x_{2}\\m_{2}\neq 0\text{, }&m_{1}=0\text{ and }x_{2}=34\\m_{2}\neq -\frac{m_{1}}{2}\text{, }&x_{1}=34\text{ and }x_{2}=34\end{matrix}\right.$$