The next proportion must be satisfied
[tex]\frac{CW}{WA}=\frac{CG}{GT}[/tex]
Replacing with data,
[tex]\begin{gathered} \frac{x+5}{12}=\frac{2}{x} \\ (x+5)\cdot x=2\cdot12 \\ x^2+5x=24 \\ x^2+5x-24=0 \end{gathered}[/tex]
Using quadratic formula,
[tex]\begin{gathered} x_{1,2}=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x_{1,2}=\frac{-5\pm\sqrt[]{5^2-4\cdot1\cdot(-24)}}{2\cdot1} \\ x_{1,2}=\frac{-5\pm\sqrt[]{25^{}+96}}{2} \\ x_{1,2}=\frac{-5\pm\sqrt[]{121}}{2} \\ x_1=\frac{-5+11}{2}=3 \\ x_2=\frac{-5-11}{2}=-8 \end{gathered}[/tex]
The negative answer has no sense in this problem, then the length of TG is 3.
