Solve x^6-2y=5

$$x ^ { 6 } - 2 y = 5$$

Solve for y

$$y=\frac{x^{6}-5}{2}$$

Steps for Solving Linear Equation

Subtract x^{6} from both sides.

$$-2y=5-x^{6}$$

Divide both sides by -2.

$$\frac{-2y}{-2}=\frac{5-x^{6}}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$y=\frac{5-x^{6}}{-2}$$

Divide 5-x^{6} by -2.

$$y=\frac{x^{6}-5}{2}$$

Solve for x (complex solution)

$$x\in e^{\frac{\pi i}{3}}\sqrt[6]{2y+5},\sqrt[6]{2y+5},e^{\frac{2\pi i}{3}}\sqrt[6]{2y+5},-\sqrt[6]{2y+5},e^{\frac{4\pi i}{3}}\sqrt[6]{2y+5},e^{\frac{5\pi i}{3}}\sqrt[6]{2y+5}$$

Solve for x

$$x=\sqrt[6]{2y+5}$$

$$x=-\sqrt[6]{2y+5}\text{, }y\geq -\frac{5}{2}$$