Solve Q=2Q^2-4Q+15omega

$$Q = 2 Q ^ { 2 } - 4 Q + 15 \omega$$

Solve for ω

$$\omega =-\frac{Q\left(2Q-5\right)}{15}$$

Steps for Solving Linear Equation

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

$$2Q^{2}-4Q+15\omega =Q$$

Subtract 2Q^{2} from both sides.

$$-4Q+15\omega =Q-2Q^{2}$$

Add 4Q to both sides.

$$15\omega =Q-2Q^{2}+4Q$$

Combine Q and 4Q to get 5Q.

$$15\omega =5Q-2Q^{2}$$

Divide both sides by 15.

$$\frac{15\omega }{15}=\frac{Q\left(5-2Q\right)}{15}$$

Dividing by 15 undoes the multiplication by 15.

$$\omega =\frac{Q\left(5-2Q\right)}{15}$$

Solve for Q

$$Q=\frac{-\sqrt{25-120\omega }+5}{4}$$

$$Q=\frac{\sqrt{25-120\omega }+5}{4}\text{, }\omega \leq \frac{5}{24}$$