In order to find the answer you first write the statement of the question in an algebraic form. Just as follow:
[tex]\begin{gathered} x+\frac{2}{x}=\frac{11}{3} \\ x^2+2=\frac{11}{3}x \\ x^2-\frac{11}{3}x+2=0 \end{gathered}[/tex]Then, you obtained a quadratic equation. The general form of a quadratic equation is:
[tex]ax^2+bx+c=0[/tex]where a=1, b=-11/13 and c=2
The quadrativ formula is:
[tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]you replace:
[tex]\begin{gathered} x=\frac{-(11/3)\pm\sqrt{(11/3)^2-4(1)(2)}}{2(1)}=\frac{-11/3\pm2.33}{2} \\ x_1=-3 \\ x_2=0.66 \end{gathered}[/tex]