Solve left|3a+4right|/sqrt{{left(frac{a-2{3}right)}^2+a^2+b}}=sqrt{frac{2/1}}{}

\frac{ \left| 3a+4 \right| }{ \sqrt{ { \left( \frac{ a-2 }{ 3 } \right) }^{ 2 } + { a }^{ 2 } +b } } = \frac{ \sqrt{ \frac{ 2 }{ 1 } } }{ }

Solve for a

\left\{\begin{matrix}a=\frac{3\sqrt{122b+472}-112}{61}\text{, }&\left(b\geq -\frac{236}{61}\text{ and }\frac{3\sqrt{122b+472}}{61}+\frac{3\sqrt{-10b-4}}{10}\leq \frac{621}{305}\text{ and }b<-\frac{244}{81}\right)\text{ or }b>-\frac{2}{5}\text{ or }\left(\frac{3\sqrt{122b+472}-112}{61}\geq \frac{\sqrt{-360b-144}}{20}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}-112}{61}\geq \frac{3\sqrt{9\left(-\frac{40b}{9}\right)-16}}{20}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}-112}{61}>\frac{3\sqrt{-10b-4}}{10}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}}{61}+\frac{3\sqrt{-10b-4}}{10}\leq \frac{621}{305}\text{ and }b<-\frac{2}{5}\text{ and }b>-\frac{244}{81}\right)\text{ or }\left(\frac{3\sqrt{122b+472}-112}{61}\geq \frac{\sqrt{-360b-144}}{20}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}-112}{61}\geq \frac{3\sqrt{9\left(-\frac{40b}{9}\right)-16}}{20}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}-112}{61}>\frac{3\sqrt{-10b-4}}{10}+\frac{1}{5}\text{ and }\frac{3\sqrt{122b+472}}{61}-\frac{3\sqrt{-10b-4}}{10}\geq \frac{621}{305}\text{ and }b<-\frac{2}{5}\text{ and }b>-\frac{244}{81}\right)\text{ or }\left(b\leq -\frac{2}{5}\text{ and }\frac{3\sqrt{122b+472}}{61}-\frac{3\sqrt{-10b-4}}{10}\geq \frac{621}{305}\text{ and }b>-\frac{244}{81}\right)\text{ or }\left(b\leq -\frac{2}{5}\text{ and }\frac{3\sqrt{122b+472}}{61}+\frac{3\sqrt{-10b-4}}{10}\leq \frac{621}{305}\text{ and }b>-\frac{244}{81}\right)\\a=\frac{-3\sqrt{122b+472}-112}{61}\text{, }&\left(-\frac{3\sqrt{122b+472}}{61}+\frac{3\sqrt{-10b-4}}{10}\leq \frac{621}{305}\text{ or }b>-\frac{244}{81}\right)\text{ and }b\geq -\frac{236}{61}\text{ and }\left(b>-\frac{2}{5}\text{ or }-\frac{3\sqrt{122b+472}}{61}+\frac{3\sqrt{-10b-4}}{10}\leq \frac{621}{305}\right)\end{matrix}\right.