Solve 0.6(a^3-b^3)-3(a-b)>0

$$0.6 ( a ^ { 3 } - b ^ { 3 } ) - 3 ( a - b ) > 0$$

Solve for b

$$\left\{\begin{matrix}b<a\text{, }&|a|>\frac{2\sqrt{15}}{3}\text{ or }\left(a>-\frac{2\sqrt{15}}{3}\text{ and }a<-\frac{\sqrt{15}}{3}\right)\\b<\frac{-\sqrt{20-3a^{2}}-a}{2}\text{, }&a\geq -\frac{\sqrt{15}}{3}\text{ and }|a|<\frac{2\sqrt{15}}{3}\\b\in \left(\frac{\sqrt{20-3a^{2}}-a}{2},a\right)\text{, }&a>\frac{\sqrt{15}}{3}\text{ and }a<\frac{2\sqrt{15}}{3}\\b\in \left(-\infty,-\frac{\sqrt{15}}{3}\right)\cup \left(-\frac{\sqrt{15}}{3},\frac{2\sqrt{15}}{3}\right)\text{, }&a=\frac{2\sqrt{15}}{3}\\b<-\frac{2\sqrt{15}}{3}\text{, }&a=-\frac{2\sqrt{15}}{3}\\b\in \left(\frac{-\sqrt{20-3a^{2}}-a}{2},\frac{\sqrt{20-3a^{2}}-a}{2}\right)\text{, }&a>-\frac{2\sqrt{15}}{3}\text{ and }a\leq -\frac{\sqrt{15}}{3}\\b\in \left(a,\frac{\sqrt{20-3a^{2}}-a}{2}\right)\text{, }&|a|<\frac{\sqrt{15}}{3}\text{ or }\left(a>-\frac{\sqrt{15}}{3}\text{ and }a\leq 0\right)\end{matrix}\right.$$

Solve for a

$$\left\{\begin{matrix}a\in \left(b,\frac{-\sqrt{20-3b^{2}}-b}{2}\right)\text{, }&b>-\frac{2\sqrt{15}}{3}\text{ and }b<-\frac{\sqrt{15}}{3}\\a>b\text{, }&|b|>\frac{2\sqrt{15}}{3}\text{ or }\left(b>\frac{\sqrt{15}}{3}\text{ and }b<\frac{2\sqrt{15}}{3}\right)\\a>\frac{\sqrt{20-3b^{2}}-b}{2}\text{, }&b\leq \frac{\sqrt{15}}{3}\text{ and }|b|<\frac{2\sqrt{15}}{3}\\a>\frac{2\sqrt{15}}{3}\text{, }&b=\frac{2\sqrt{15}}{3}\\a\in \left(-\frac{2\sqrt{15}}{3},\frac{\sqrt{15}}{3}\right)\cup \left(\frac{\sqrt{15}}{3},\infty\right)\text{, }&b=-\frac{2\sqrt{15}}{3}\\a\in \left(\frac{-\sqrt{20-3b^{2}}-b}{2},\frac{\sqrt{20-3b^{2}}-b}{2}\right)\text{, }&b\geq \frac{\sqrt{15}}{3}\text{ and }b<\frac{2\sqrt{15}}{3}\\a\in \left(\frac{-\sqrt{20-3b^{2}}-b}{2},b\right)\text{, }&\left(b\geq 0\text{ and }b<\frac{\sqrt{15}}{3}\right)\text{ or }|b|<\frac{\sqrt{15}}{3}\end{matrix}\right.$$