Solve n^3+y^3/ny=52/1

$$\frac { n ^ { 3 } + y ^ { 3 } } { n y } = \frac { 52 } { 1 }$$

Solve for n (complex solution)

$$n=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}\right)^{-\frac{1}{3}}\left(3\left(-\sqrt{3}i-1\right)\times \left(\frac{\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}}{9}\right)^{\frac{2}{3}}+104\times 2^{\frac{2}{3}}y\right)}{8}$$

$$n=\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}\right)^{-\frac{1}{3}}\left(3\times \left(\frac{\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}}{9}\right)^{\frac{2}{3}}+52\times 2^{\frac{2}{3}}y\right)}{2}$$

$$n=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}\right)^{-\frac{1}{3}}\left(3\left(-1+\sqrt{3}i\right)\times \left(\frac{\sqrt{3y^{3}\left(27y^{3}-562432\right)}-9y^{3}}{9}\right)^{\frac{2}{3}}+104\times 2^{\frac{2}{3}}y\right)}{8}\text{, }y\neq 0$$

Solve for y (complex solution)

$$y=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}\right)^{-\frac{1}{3}}\left(3\left(-\sqrt{3}i-1\right)\times \left(\frac{\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}}{9}\right)^{\frac{2}{3}}+104\times 2^{\frac{2}{3}}n\right)}{8}$$

$$y=\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}\right)^{-\frac{1}{3}}\left(3\times \left(\frac{\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}}{9}\right)^{\frac{2}{3}}+52\times 2^{\frac{2}{3}}n\right)}{2}$$

$$y=-\frac{3\times \left(\frac{2}{9}\right)^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}\right)^{-\frac{1}{3}}\left(3\left(-1+\sqrt{3}i\right)\times \left(\frac{\sqrt{3n^{3}\left(27n^{3}-562432\right)}-9n^{3}}{9}\right)^{\frac{2}{3}}+104\times 2^{\frac{2}{3}}n\right)}{8}\text{, }n\neq 0$$