Answer
$x_{1}=-\dfrac {4}{3};x_{2}=5$
Work Step by Step
$\log _{4}\left[ \left( 3x+1\right) \left( x-4\right) \right] =2\Rightarrow \left( 3x+1\right) \left( x-4\right) =4^{2}\Rightarrow 3x^{2}-11x-4=16$
$\Rightarrow 3x^{2}-11x-20=0\Rightarrow \left( 3x+4\right) \left( x-5\right) =0\Rightarrow $
$x_{1}=-\dfrac {4}{3};x_{2}=5$
