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The non-complex solution is not nice (the complex ones are worse) \begin{equation}  x = \frac{2r}{3\beta}+\frac{1}{3\sqrt[3]{2}\beta^3}\bigg(\sqrt[3]{-20r^3\beta^6+72r^2\beta^6+\sqrt{4(2r^2\beta^4+6r\beta^4)^3+(-20r^3\beta^6+72r^2\beta^6-108\beta^6)^2}-108\beta^6}\bigg) \frac{2r}{3\beta}+\frac{1}{3\sqrt[3]{2}\beta^3}\bigg(\sqrt[3]{K+\sqrt{4R^3+(K-108\beta^6)^2}-108\beta^6}\bigg)  \\ -\frac{\sqrt[3]{2}(2r^2\beta^4+6r\beta^4)}{\bigg(3\beta^3\sqrt[3]{-20r^3\beta^6+72r^2\beta^6+\sqrt{4(2r^2\beta^4+6r\beta^4)^3+(-20r^3\beta^6+72r^2\beta^6-108\beta^6)^2}-108\beta^6}\bigg)} -\frac{\sqrt[3]{2}R}{\bigg(3\beta^3\sqrt[3]{K+\sqrt{4R^3+(K-108\beta^6)^2}-108\beta^6}\bigg)}  \end{equation}  Where \begin{equation}  K=-20r^3\beta^6+72r^2\beta^6 \\  R=2r^2\beta^4+6r\beta^4  \end{equation}