Solve eta^2=-18-9n

$$\eta ^ { 2 } = - 18 - 9 n$$

Solve for n

$$n=-\frac{\eta ^{2}}{9}-2$$

Steps for Solving Linear Equation

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

$$-18-9n=\eta ^{2}$$

Add 18 to both sides.

$$-9n=\eta ^{2}+18$$

Divide both sides by -9.

$$\frac{-9n}{-9}=\frac{\eta ^{2}+18}{-9}$$

Dividing by -9 undoes the multiplication by -9.

$$n=\frac{\eta ^{2}+18}{-9}$$

Divide \eta ^{2}+18 by -9.

$$n=-\frac{\eta ^{2}}{9}-2$$

Solve for η

$$\eta =3\sqrt{-n-2}$$

$$\eta =-3\sqrt{-n-2}\text{, }n\leq -2$$