#### Answer

$\dfrac {5}{3}\left( 1\pm \sqrt {13}\right) $

#### Work Step by Step

$\log _{4}\left[ \left( 3x+8\right) \left( x-6\right) \right] =3\Rightarrow \left( 3x+8\right) \left( x-6\right) =4^{3}$
$\Rightarrow 3x^{2}-10x-48=64\Rightarrow 3x^{2}-10x-100=0$
$x_{1,2}=\dfrac {-b\pm \sqrt {b^{2}-4ac}}{2a}=\dfrac {10\pm \sqrt {\left( -10\right) ^{2}+4\times 3\times 100}}{2\times 3}=\dfrac {10\pm 10\sqrt {13}}{6}=\dfrac {5}{3}\left( 1\pm \sqrt {13}\right) $