Solve (3p+1)x-p(4+x^2)>0

$$( 3 p + 1 ) x - p ( 4 + x ^ { 2 } ) > 0$$

Solve for x

$$\left\{\begin{matrix}x\neq -2\text{, }&p=-\frac{1}{7}\\x\in \mathrm{R}\text{, }&p<-\frac{1}{7}\\x\in \left(-\infty,\frac{\sqrt{\left(1-p\right)\left(7p+1\right)}+3p+1}{2p}\right)\cup \left(-\frac{\sqrt{\left(1-p\right)\left(7p+1\right)}-3p-1}{2p},\infty\right)\text{, }&p>-\frac{1}{7}\text{ and }p<0\\x>0\text{, }&p=0\\x\in \left(-\frac{\sqrt{\left(1-p\right)\left(7p+1\right)}-3p-1}{2p},\frac{\sqrt{\left(1-p\right)\left(7p+1\right)}+3p+1}{2p}\right)\text{, }&p>0\text{ and }p<1\end{matrix}\right.$$

Solve for p

$$p<-\frac{x}{-x^{2}+3x-4}$$