Solve y=(sqrt{2x-1}+3x)^4

$$y = ( \sqrt { 2 x - 1 } + 3 x ) ^ { 4 }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{i\sqrt[4]{y}}{3}+\frac{\sqrt{-6i\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{; }x=-\frac{i\sqrt[4]{y}}{3}-\frac{\sqrt{-6i\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{, }&arg(3x+i\sqrt[4]{y})\geq \pi \\x=-\frac{\sqrt[4]{y}}{3}+\frac{\sqrt{-6\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{; }x=-\frac{\sqrt[4]{y}}{3}-\frac{\sqrt{-6\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{, }&arg(3x+\sqrt[4]{y})\geq \pi \\x=\frac{1}{2}=0.5\text{, }&y=\frac{81}{16}\\x=\frac{\sqrt[4]{y}}{3}-\frac{\sqrt{6\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{; }x=\frac{\sqrt[4]{y}}{3}+\frac{\sqrt{6\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{, }&arg(3x-\sqrt[4]{y})\geq \pi \\x=\frac{i\sqrt[4]{y}}{3}+\frac{\sqrt{6i\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{; }x=\frac{i\sqrt[4]{y}}{3}-\frac{\sqrt{6i\sqrt[4]{y}-8}}{9}+\frac{1}{9}\text{, }&arg(3x-i\sqrt[4]{y})\geq \pi \end{matrix}\right.$$

Solve for y (complex solution)

$$y=\left(3x+\sqrt{2x-1}\right)^{4}$$

Solve for x

$$x=\frac{\sqrt[4]{y}}{3}-\frac{\sqrt{6\sqrt[4]{y}-8}}{9}+\frac{1}{9}$$

$$y\geq \frac{81}{16}$$

Solve for y

$$y=\left(3x+\sqrt{2x-1}\right)^{4}$$

$$x\geq \frac{1}{2}$$