Solve E-1/R^2=2

$$E - \frac { 1 } { R ^ { 2 } } = 2$$

Solve for E

$$E=2+\frac{1}{R^{2}}$$

$$R\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by R^{2}.

$$R^{2}E-1=2R^{2}$$

Add 1 to both sides.

$$R^{2}E=2R^{2}+1$$

Divide both sides by R^{2}.

$$\frac{R^{2}E}{R^{2}}=\frac{2R^{2}+1}{R^{2}}$$

Dividing by R^{2} undoes the multiplication by R^{2}.

$$E=\frac{2R^{2}+1}{R^{2}}$$

Divide 2R^{2}+1 by R^{2}.

$$E=2+\frac{1}{R^{2}}$$

Solve for R (complex solution)

$$R=-\left(E-2\right)^{-\frac{1}{2}}$$

$$R=\left(E-2\right)^{-\frac{1}{2}}\text{, }E\neq 2$$

Solve for R

$$R=\frac{1}{\sqrt{E-2}}$$

$$R=-\frac{1}{\sqrt{E-2}}\text{, }E>2$$