Solve y^7-9+n/4=-7

$$y ^ { 7 } - 9 + \frac { n } { 4 } = - 7$$

Solve for n

$$n=8-4y^{7}$$

Solution Steps

Multiply both sides of the equation by 4.

$$4y^{7}-36+n=-28$$

Subtract 4y^{7} from both sides.

$$-36+n=-28-4y^{7}$$

Add 36 to both sides.

$$n=-28-4y^{7}+36$$

Add -28 and 36 to get 8.

$$n=8-4y^{7}$$

Solve for y (complex solution)

$$y\in \frac{4^{\frac{6}{7}}e^{\frac{2i\pi }{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}e^{\frac{4i\pi }{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}e^{\frac{6i\pi }{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}e^{\frac{8i\pi }{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}e^{\frac{10i\pi }{7}}\sqrt[7]{8-n}}{4},\frac{4^{\frac{6}{7}}e^{\frac{12i\pi }{7}}\sqrt[7]{8-n}}{4}$$

Solve for y

$$y=\frac{4^{\frac{6}{7}}\sqrt[7]{8-n}}{4}$$