Solve 76.7V=18.81*R/R_{1+21Omega}

$$76.7 V = 18.81 \cdot \frac { R } { R _ { 1 } + 21 \Omega }$$

Solve for R

$$R=V\left(\frac{7670R_{1}}{1881}+\frac{53690\Omega }{627}\right)$$

$$R_{1}\neq -21\Omega$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R_{1}+21\Omega .

$$76.7V\left(R_{1}+21\Omega \right)=18.81R$$

Use the distributive property to multiply 76.7V by R_{1}+21\Omega .

$$76.7VR_{1}+1610.7\Omega V=18.81R$$

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

$$18.81R=76.7VR_{1}+1610.7\Omega V$$

The equation is in standard form.

$$18.81R=\frac{767R_{1}V+16107V\Omega }{10}$$

Divide both sides of the equation by 18.81, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{18.81R}{18.81}=\frac{V\times \frac{767R_{1}+16107\Omega }{10}}{18.81}$$

Dividing by 18.81 undoes the multiplication by 18.81.

$$R=\frac{V\times \frac{767R_{1}+16107\Omega }{10}}{18.81}$$

Divide V\times \frac{767R_{1}+16107\Omega }{10} by 18.81 by multiplying V\times \frac{767R_{1}+16107\Omega }{10} by the reciprocal of 18.81.

$$R=\frac{7670V\left(R_{1}+21\Omega \right)}{1881}$$

Solve for R_1

$$\left\{\begin{matrix}R_{1}=-21\Omega +\frac{1881R}{7670V}\text{, }&R\neq 0\text{ and }V\neq 0\\R_{1}\neq -21\Omega \text{, }&V=0\text{ and }R=0\end{matrix}\right.$$