Solve (1+k/4n)=sqrt{e}

$$( 1 + \frac { k } { 4 n } ) = \sqrt { e }$$

Solve for n

$$n=\frac{k}{4\left(\sqrt{e}-1\right)}$$

$$k\neq 0$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 4n.

$$4n+k=4n\sqrt{e}$$

Subtract 4n\sqrt{e} from both sides.

$$4n+k-4n\sqrt{e}=0$$

Subtract k from both sides. Anything subtracted from zero gives its negation.

$$4n-4n\sqrt{e}=-k$$

Combine all terms containing n.

$$\left(4-4\sqrt{e}\right)n=-k$$

The equation is in standard form.

$$\left(-4\sqrt{e}+4\right)n=-k$$

Divide both sides by 4-4\sqrt{e}.

$$\frac{\left(-4\sqrt{e}+4\right)n}{-4\sqrt{e}+4}=-\frac{k}{-4\sqrt{e}+4}$$

Dividing by 4-4\sqrt{e} undoes the multiplication by 4-4\sqrt{e}.

$$n=-\frac{k}{-4\sqrt{e}+4}$$

Divide -k by 4-4\sqrt{e}.

$$n=\frac{k}{4\left(\sqrt{e}-1\right)}$$

Variable n cannot be equal to 0.

$$n=\frac{k}{4\left(\sqrt{e}-1\right)}\text{, }n\neq 0$$

Solve for k

$$k=4\left(\sqrt{e}-1\right)n$$

$$n\neq 0$$