Solve {l}{-2dsqrt{2d}+3a^2sqrt{2}+a<0}{2dsqrt{2a}-3d^2sqrt{2a}+a>0}

$$\left\{ \begin{array} { l } { - 2 d \sqrt { 2 d } + 3 a ^ { 2 } \sqrt { 2 } + a < 0 } \\ { 2 d \sqrt { 2 a } - 3 d ^ { 2 } \sqrt { 2 a } + a > 0 } \end{array} \right.$$

Solve for d

$$\left\{\begin{matrix}d\in \left(-\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3},\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3}\right)\text{, }&a>0\text{ and }-\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3}\geq \frac{\left(3\sqrt{2}a^{2}+a\right)^{\frac{2}{3}}}{2}\\d\in \left(\frac{\left(3\sqrt{2}a^{2}+a\right)^{\frac{2}{3}}}{2},\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3}\right)\text{, }&a>0\text{ and }\frac{\left(3\sqrt{2}a^{2}+a\right)^{\frac{2}{3}}}{2}<\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3}\text{ and }-\frac{2^{\frac{3}{4}}\sqrt{3\sqrt{a}+\sqrt{2}}}{6}+\frac{1}{3}<\frac{\left(3\sqrt{2}a^{2}+a\right)^{\frac{2}{3}}}{2}\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a\in \left(0,\frac{\sqrt{2}\left(\sqrt{48d^{\frac{3}{2}}+1}-1\right)}{12}\right)\text{, }&d>0\text{ and }d\leq \frac{2}{3}\\a\in \left(2\left(d\left(3d-2\right)\right)^{2},\frac{\sqrt{2}\left(\sqrt{48d^{\frac{3}{2}}+1}-1\right)}{12}\right)\text{, }&d\geq 0\text{ and }\left(3\sqrt{2}d^{2}-2\sqrt{2}d\right)^{2}<\frac{\sqrt{2}\left(\sqrt{48d^{\frac{3}{2}}+1}-1\right)}{12}\end{matrix}\right.$$