Solve n=90/n

$$n = \frac { 90 } { n }$$

Solve for n

$$n=3\sqrt{10}\approx 9.486832981$$

$$n=-3\sqrt{10}\approx -9.486832981$$

Steps by Finding Square Root

Subtract \frac{90}{n} from both sides.

$$n-\frac{90}{n}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{n}{n}.

$$\frac{nn}{n}-\frac{90}{n}=0$$

Since \frac{nn}{n} and \frac{90}{n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{nn-90}{n}=0$$

Do the multiplications in nn-90.

$$\frac{n^{2}-90}{n}=0$$

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

$$n^{2}-90=0$$

Add 90 to both sides. Anything plus zero gives itself.

$$n^{2}=90$$

Take the square root of both sides of the equation.

$$n=3\sqrt{10} n=-3\sqrt{10}$$

Steps Using the Quadratic Formula

Subtract \frac{90}{n} from both sides.

$$n-\frac{90}{n}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply n times \frac{n}{n}.

$$\frac{nn}{n}-\frac{90}{n}=0$$

Since \frac{nn}{n} and \frac{90}{n} have the same denominator, subtract them by subtracting their numerators.

$$\frac{nn-90}{n}=0$$

Do the multiplications in nn-90.

$$\frac{n^{2}-90}{n}=0$$

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

$$n^{2}-90=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -90 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$n=\frac{0±\sqrt{0^{2}-4\left(-90\right)}}{2}$$

Square 0.

$$n=\frac{0±\sqrt{-4\left(-90\right)}}{2}$$

Multiply -4 times -90.

$$n=\frac{0±\sqrt{360}}{2}$$

Take the square root of 360.

$$n=\frac{0±6\sqrt{10}}{2}$$

Now solve the equation n=\frac{0±6\sqrt{10}}{2} when ± is plus.

$$n=3\sqrt{10}$$

Now solve the equation n=\frac{0±6\sqrt{10}}{2} when ± is minus.

$$n=-3\sqrt{10}$$

The equation is now solved.

$$n=3\sqrt{10} n=-3\sqrt{10}$$