[tex]\frac{3x-12}{x-5}=-7\\\frac{3x-12}{x-5}\left(x-5\right)=-7\left(x-5\right)\\3x-12=-7\left(x-5\right)\\3x-12=-7x+35\\3x-12+12=-7x+35+12\\3x=-7x+47\\3x+7x=-7x+47+7x\\10x=47\\\frac{10x}{10}=\frac{47}{10}\\x=\frac{47}{10}\\\\\boxed{x=4\frac{7}{10} }[/tex]
