$4x+1=3x\left(pra^{2}+1\right)\text{ and }3x\left(pra^{2}+1\right)=2$

$x=-\frac{1}{1-3pra^{2}}$
$p\neq \frac{1}{3ra^{2}}\text{ and }p\neq -\frac{1}{ra^{2}}\text{ and }\left(p<0\text{ or }r>0\right)\text{ and }r\neq 0\text{ and }p\neq 0\text{ and }\left(r<0\text{ or }p>0\right)\text{ and }|a|=\frac{5}{\sqrt{15pr}}$

$r=\frac{5}{3pa^{2}}$
$x=\frac{1}{4}\text{ and }a\neq 0\text{ and }p\neq 0$