[tex]\dfrac{x}{q}+x+xq=39\\\\
\dfrac{9}{q}+9+9q=39\\\\
\dfrac{9}{q}+9q=30\\\\
9+9q^2=30q\\\\
3+3q^2=10q\\\\
3q^2-10q+3=0\\\\
\Delta=b^2-4\cdot a\cdot c\\
\Delta=(-10)-4\cdot3\cdot3\\
\Delta=100-36\\
\Delta=64\\\\
q=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{10\pm\sqrt{64}}{2\cdot3}=\dfrac{10\pm8}{6}=\dfrac{5\pm4}{3}\Lonrightarrow\begin{cases}q_1=\frac{9}{3}=3\\q_2=\frac{1}{3}\end{cases}[/tex]
[tex]S=\{\dfrac{1}{3},3\}[/tex]
