$M=\dfrac{20-x}{x-12}$ $\text{đạt GTNN}$
$⇔\dfrac{x-20}{x-12}$ $\text{đạt GTNN}$
$⇔\dfrac{-(x-12)+8}{x-12}$ $\text{đạt GTNN}$
$⇔-1+\dfrac{8}{x-12}$ $\text{đạt GTNN}$
$\text{Để M đặt GTNN thì }$ $⇔\dfrac{8}{x-12}$ $\text{đạt GTNN}$
$⇔x-12$ $\text{là số âm lớn nhất}$
$⇔x-12=-1$ $\text{đạt GTNN}$
$⇔x=11$
$\text{Vậy M đạt GTNN khi x=11}$