$\left\{\begin{matrix}x=\frac{6^{\frac{2}{3}}\left(1+\sqrt{3}i\right)\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)^{-\frac{1}{3}}\left(\left(1+\sqrt{3}i\right)\times \left(3\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)\right)^{\frac{2}{3}}+6\times 2^{\frac{2}{3}}c\right)}{72}\text{; }x=\frac{6^{\frac{2}{3}}\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)^{-\frac{1}{3}}\left(\left(3\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)\right)^{\frac{2}{3}}-3\times 2^{\frac{2}{3}}c\right)}{18}\text{; }x=\frac{6^{\frac{2}{3}}\left(-\sqrt{3}i+1\right)\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)^{-\frac{1}{3}}\left(\left(-\sqrt{3}i+1\right)\times \left(3\left(\sqrt{3\left(27b^{2}+4c^{3}\right)}+9b\right)\right)^{\frac{2}{3}}+6\times 2^{\frac{2}{3}}c\right)}{72}\text{, }&c\neq 0\text{ and }a=c\text{ and }d=8\\x=\frac{\left(-1+\sqrt{3}i\right)\sqrt[3]{b}}{2}\text{; }x=\sqrt[3]{b}\text{; }x=-\frac{\left(1+\sqrt{3}i\right)\sqrt[3]{b}}{2}\text{, }&a=0\text{ and }c=0\text{ and }d=8\end{matrix}\right.$