Solve for b
\left\{\begin{matrix}b>-\frac{a\left(2a+1\right)}{3-2a}\text{, }&a<\frac{3}{2}\\b\in \mathrm{R}\text{, }&a=\frac{3}{2}\\b<-\frac{a\left(2a+1\right)}{3-2a}\text{, }&a>\frac{3}{2}\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a\neq \frac{3}{2}-\sqrt{3}\text{, }&b=\frac{7}{2}-2\sqrt{3}\\a\neq \sqrt{3}+\frac{3}{2}\text{, }&b=2\sqrt{3}+\frac{7}{2}\\a\in \mathrm{R}\text{, }&b>\frac{7}{2}-2\sqrt{3}\text{ and }b<2\sqrt{3}+\frac{7}{2}\\a\in \left(\frac{\sqrt{4b^{2}-28b+1}}{4}+\frac{b}{2}-\frac{1}{4},\infty\right)\cup \left(-\infty,-\frac{\sqrt{4b^{2}-28b+1}}{4}+\frac{b}{2}-\frac{1}{4}\right)\text{, }&b<\frac{7}{2}-2\sqrt{3}\text{ or }b>2\sqrt{3}+\frac{7}{2}\end{matrix}\right.
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