Solve V_{L}=frac{V_{1}R_{1}}{R_{1}+R_{2}}quadw

$$V _ { L } = \frac { V _ { 1 } R _ { 1 } } { R _ { 1 } + R _ { 2 } } \quad w$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=\frac{R_{2}V_{L}}{V_{1}w-V_{L}}\text{, }&R_{2}\neq 0\text{ and }w\neq 0\text{ and }V_{1}\neq 0\text{ and }V_{L}\neq V_{1}w\\R_{1}\neq 0\text{, }&R_{2}=0\text{ and }V_{L}=V_{1}w\text{ and }w\neq 0\text{ and }V_{1}\neq 0\\R_{1}\neq -R_{2}\text{, }&\left(V_{1}=0\text{ or }w=0\right)\text{ and }V_{L}=0\end{matrix}\right.$$

Solve for R_2

$$\left\{\begin{matrix}R_{2}=\frac{R_{1}\left(V_{1}w-V_{L}\right)}{V_{L}}\text{, }&w\neq 0\text{ and }R_{1}\neq 0\text{ and }V_{1}\neq 0\text{ and }V_{L}\neq 0\\R_{2}\neq -R_{1}\text{, }&\left(w=0\text{ or }V_{1}=0\right)\text{ and }\left(w=0\text{ or }R_{1}\neq 0\right)\text{ and }V_{L}=0\\R_{2}\neq 0\text{, }&V_{L}=0\text{ and }R_{1}=0\end{matrix}\right.$$