Solve for x
x>\frac{\left(a+1\right)\left(a+4\right)}{5a+4}
a\neq -\frac{4}{5}
Solve for a
\left\{\begin{matrix}a\in \left(\frac{-\sqrt{\left(x-1\right)\left(25x-9\right)}+5x-5}{2},\frac{\sqrt{\left(x-1\right)\left(25x-9\right)}+5x-5}{2}\right)\text{, }&x>1\\a\in \left(-\infty,-\frac{8}{5}\right)\cup \left(-\frac{8}{5},-\frac{4}{5}\right)\text{, }&x=\frac{9}{25}\\a<-\frac{4}{5}\text{, }&x>1\text{ or }\left(x>\frac{9}{25}\text{ and }x\leq 1\right)\\a\in \left(\frac{\sqrt{\left(x-1\right)\left(25x-9\right)}+5x-5}{2},-\frac{4}{5}\right)\cup \left(-\infty,\frac{-\sqrt{\left(x-1\right)\left(25x-9\right)}+5x-5}{2}\right)\text{, }&x<\frac{9}{25}\end{matrix}\right.
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