Solve for q (complex solution)
q\in 2^{\frac{3}{4}}\times 3^{\frac{7}{8}}\left(\frac{1}{6}+\frac{1}{6}i\right)\sqrt[8]{P},\frac{3^{\frac{7}{8}}\sqrt[4]{2}\sqrt[8]{P}}{3},\frac{3^{\frac{7}{8}}\sqrt[4]{2}i\sqrt[8]{P}}{3},2^{\frac{3}{4}}\times 3^{\frac{7}{8}}\left(-\frac{1}{6}+\frac{1}{6}i\right)\sqrt[8]{P},-\frac{3^{\frac{7}{8}}\sqrt[4]{2}\sqrt[8]{P}}{3},2^{\frac{3}{4}}\times 3^{\frac{7}{8}}\left(-\frac{1}{6}-\frac{1}{6}i\right)\sqrt[8]{P},-\frac{3^{\frac{7}{8}}\sqrt[4]{2}i\sqrt[8]{P}}{3},2^{\frac{3}{4}}\times 3^{\frac{7}{8}}\left(\frac{1}{6}-\frac{1}{6}i\right)\sqrt[8]{P}
Solve for P
P=\frac{3q^{8}}{4}
Solve for q
q=\frac{3^{\frac{7}{8}}\sqrt[4]{2}\sqrt[8]{P}}{3}
q=-\frac{3^{\frac{7}{8}}\sqrt[4]{2}\sqrt[8]{P}}{3}\text{, }P\geq 0
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