Solve 200V-3000/v^2-255+200/V=30

$$\frac { 200 V - 3000 } { v ^ { 2 } - 255 } + \frac { 200 } { V } = 30$$

Solve for V (complex solution)

$$V=\frac{\sqrt{9v^{4}-4390v^{2}+624225}}{40}+\frac{3v^{2}}{40}-\frac{93}{8}$$

$$V=-\frac{\sqrt{9v^{4}-4390v^{2}+624225}}{40}+\frac{3v^{2}}{40}-\frac{93}{8}\text{, }v\neq -\sqrt{255}\text{ and }v\neq \sqrt{255}$$

Solve for v (complex solution)

$$v=-i\left(20-3V\right)^{-\frac{1}{2}}\sqrt{20V^{2}+465V-5100}$$

$$v=i\left(20-3V\right)^{-\frac{1}{2}}\sqrt{20V^{2}+465V-5100}\text{, }V\neq 15\text{ and }V\neq 0\text{ and }V\neq \frac{20}{3}$$

Solve for V

$$V=\frac{\sqrt{9v^{4}-4390v^{2}+624225}}{40}+\frac{3v^{2}}{40}-\frac{93}{8}$$

$$V=-\frac{\sqrt{9v^{4}-4390v^{2}+624225}}{40}+\frac{3v^{2}}{40}-\frac{93}{8}\text{, }|v|\neq \sqrt{255}$$

Solve for v

$$v=\sqrt{-\frac{5\left(4V^{2}+93V-1020\right)}{20-3V}}$$

$$v=-\sqrt{-\frac{5\left(4V^{2}+93V-1020\right)}{20-3V}}\text{, }\left(V\neq 15\text{ and }V\geq \frac{\sqrt{24969}-93}{8}\right)\text{ or }\left(V\neq 0\text{ and }V\geq \frac{-\sqrt{24969}-93}{8}\text{ and }V<\frac{20}{3}\right)$$