Solve θ=(2/3sqrt[3]{x}-5/3sqrt[3]{x^2})

$$\theta = ( \frac { 2 } { 3 \sqrt[ 3 ] { x } } - \frac { 5 } { 3 \sqrt[ 3 ] { x ^ { 2 } } } )$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{\left(1-15\theta \right)\left(15\theta -4\right)^{2}}-45\theta +4}{27\theta ^{3}}\text{; }x=\frac{-\sqrt{\left(1-15\theta \right)\left(15\theta -4\right)^{2}}-45\theta +4}{27\theta ^{3}}\text{, }&\theta \neq 0\text{ and }|arg(3x^{\frac{2}{3}}\theta -2\sqrt[3]{x})-\pi |<\frac{2\pi }{3}\\x=\frac{125}{8}=15.625\text{, }&\theta =0\end{matrix}\right.$$

Solve for θ (complex solution)

$$\theta =\frac{2x^{-\frac{1}{3}}-5x^{-\frac{2}{3}}}{3}$$

$$x\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\left(\frac{\sqrt{1-15\theta }+1}{\theta }\right)^{3}}{27}\text{; }x=-\frac{\left(\frac{\sqrt{1-15\theta }-1}{\theta }\right)^{3}}{27}\text{, }&\theta \neq 0\text{ and }\theta \leq \frac{1}{15}\\x=\frac{125}{8}=15.625\text{, }&\theta =0\end{matrix}\right.$$

Solve for θ

$$\theta =\frac{2}{3\sqrt[3]{x}}-\frac{5}{3x^{\frac{2}{3}}}$$

$$x\neq 0$$