$|\left(2a-b\right)\left(2b-a\right)|<63$

$\left\{\begin{matrix}b\in \left(\frac{-3\sqrt{a^{2}+56}+5a}{4},\frac{3\sqrt{a^{2}+56}+5a}{4}\right)\text{, }&|a|<2\sqrt{14}\\b\in \left(\frac{5\sqrt{14}}{2}-3\sqrt{7},\frac{5\sqrt{14}}{2}\right)\cup \left(\frac{5\sqrt{14}}{2},\frac{5\sqrt{14}}{2}+3\sqrt{7}\right)\text{, }&a=2\sqrt{14}\\b\in \left(-\frac{5\sqrt{14}}{2}-3\sqrt{7},-\frac{5\sqrt{14}}{2}\right)\cup \left(-\frac{5\sqrt{14}}{2},-\frac{5\sqrt{14}}{2}+3\sqrt{7}\right)\text{, }&a=-2\sqrt{14}\\b\in \left(\frac{-3\sqrt{a^{2}+56}+5a}{4},\frac{-3\sqrt{a^{2}-56}+5a}{4}\right)\text{, }&|a|>2\sqrt{14}\text{ and }\frac{-3\sqrt{a^{2}+56}+5a}{4}<\frac{-3\sqrt{a^{2}-56}+5a}{4}\\b\in \left(\frac{3\sqrt{a^{2}-56}+5a}{4},\frac{3\sqrt{a^{2}+56}+5a}{4}\right)\text{, }&|a|>2\sqrt{14}\text{ and }\frac{3\sqrt{a^{2}-56}+5a}{4}<\frac{3\sqrt{a^{2}+56}+5a}{4}\end{matrix}\right.$

$\left\{\begin{matrix}a\in \left(\frac{-3\sqrt{b^{2}+56}+5b}{4},\frac{3\sqrt{b^{2}+56}+5b}{4}\right)\text{, }&|b|<2\sqrt{14}\\a\in \left(\frac{5\sqrt{14}}{2}-3\sqrt{7},\frac{5\sqrt{14}}{2}\right)\cup \left(\frac{5\sqrt{14}}{2},\frac{5\sqrt{14}}{2}+3\sqrt{7}\right)\text{, }&b=2\sqrt{14}\\a\in \left(-\frac{5\sqrt{14}}{2}-3\sqrt{7},-\frac{5\sqrt{14}}{2}\right)\cup \left(-\frac{5\sqrt{14}}{2},-\frac{5\sqrt{14}}{2}+3\sqrt{7}\right)\text{, }&b=-2\sqrt{14}\\a\in \left(\frac{-3\sqrt{b^{2}+56}+5b}{4},\frac{-3\sqrt{b^{2}-56}+5b}{4}\right)\text{, }&|b|>2\sqrt{14}\text{ and }\frac{-3\sqrt{b^{2}+56}+5b}{4}<\frac{-3\sqrt{b^{2}-56}+5b}{4}\\a\in \left(\frac{3\sqrt{b^{2}-56}+5b}{4},\frac{3\sqrt{b^{2}+56}+5b}{4}\right)\text{, }&|b|>2\sqrt{14}\text{ and }\frac{3\sqrt{b^{2}-56}+5b}{4}<\frac{3\sqrt{b^{2}+56}+5b}{4}\end{matrix}\right.$