Solve V_{0}=(V_{2}-V_{1})*frac{R_{2}}{R_{1}}

$$V _ { 0 } = ( V _ { 2 } - V _ { 1 } ) \cdot \frac { R _ { 2 } } { R _ { 1 } }$$

Solve for R_1

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

Steps for Solving Linear Equation

Variable R_{1} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by R_{1}.

$$V_{0}R_{1}=\left(V_{2}-V_{1}\right)R_{2}$$

Use the distributive property to multiply V_{2}-V_{1} by R_{2}.

$$V_{0}R_{1}=V_{2}R_{2}-V_{1}R_{2}$$

The equation is in standard form.

$$V_{0}R_{1}=R_{2}V_{2}-R_{2}V_{1}$$

Divide both sides by V_{0}.

$$\frac{V_{0}R_{1}}{V_{0}}=\frac{R_{2}\left(V_{2}-V_{1}\right)}{V_{0}}$$

Dividing by V_{0} undoes the multiplication by V_{0}.

$$R_{1}=\frac{R_{2}\left(V_{2}-V_{1}\right)}{V_{0}}$$

Variable R_{1} cannot be equal to 0.

$$R_{1}=\frac{R_{2}\left(V_{2}-V_{1}\right)}{V_{0}}\text{, }R_{1}\neq 0$$

Solve for R_2

$$\left\{\begin{matrix}R_{2}=\frac{R_{1}V_{0}}{V_{2}-V_{1}}\text{, }&V_{2}\neq V_{1}\text{ and }R_{1}\neq 0\\R_{2}\in \mathrm{R}\text{, }&V_{0}=0\text{ and }V_{2}=V_{1}\text{ and }R_{1}\neq 0\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{1}.

$$V_{0}R_{1}=\left(V_{2}-V_{1}\right)R_{2}$$

Use the distributive property to multiply V_{2}-V_{1} by R_{2}.

$$V_{0}R_{1}=V_{2}R_{2}-V_{1}R_{2}$$

Swap sides so that all variable terms are on the left hand side.

$$V_{2}R_{2}-V_{1}R_{2}=V_{0}R_{1}$$

Combine all terms containing R_{2}.

$$\left(V_{2}-V_{1}\right)R_{2}=V_{0}R_{1}$$

The equation is in standard form.

$$\left(V_{2}-V_{1}\right)R_{2}=R_{1}V_{0}$$

Divide both sides by V_{2}-V_{1}.

$$\frac{\left(V_{2}-V_{1}\right)R_{2}}{V_{2}-V_{1}}=\frac{R_{1}V_{0}}{V_{2}-V_{1}}$$

Dividing by V_{2}-V_{1} undoes the multiplication by V_{2}-V_{1}.

$$R_{2}=\frac{R_{1}V_{0}}{V_{2}-V_{1}}$$