Solve x^2+frac{sqrt{x}}{n}+5=1

$$x ^ { 2 } + \frac { \sqrt { x } } { n } + 5 = 1$$

Solve for n

$$n=-\frac{\sqrt{x}}{x^{2}+4}$$

$$x>0$$

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 n.

$$nx^{2}+\sqrt{x}+n\times 5=n$$

Subtract n from both sides.

$$nx^{2}+\sqrt{x}+n\times 5-n=0$$

Combine n\times 5 and -n to get 4n.

$$nx^{2}+\sqrt{x}+4n=0$$

Subtract \sqrt{x} from both sides. Anything subtracted from zero gives its negation.

$$nx^{2}+4n=-\sqrt{x}$$

Combine all terms containing n.

$$\left(x^{2}+4\right)n=-\sqrt{x}$$

Divide both sides by x^{2}+4.

$$\frac{\left(x^{2}+4\right)n}{x^{2}+4}=-\frac{\sqrt{x}}{x^{2}+4}$$

Dividing by x^{2}+4 undoes the multiplication by x^{2}+4.

$$n=-\frac{\sqrt{x}}{x^{2}+4}$$

Variable n cannot be equal to 0.

$$n=-\frac{\sqrt{x}}{x^{2}+4}\text{, }n\neq 0$$