TeX source:
\begin{array}{rclcl} (x+9)(x-9) &=& \dfrac{1}{2}(x+18)+\dfrac{11x}{2} \cr\cr x^2-81 &=& \dfrac{1}{2}(x+18)+\dfrac{11x}{2} & \vert & \cdot 2 \cr\cr 2x^2-162 &=& x+18+11x \cr\cr 2x^2-162 &=& 12x+18 & \vert & -12x-18 \cr\cr 2x^2-12x-180 &=& 0 \cr\cr x_{1,2} &=& \dfrac{12 \pm \sqrt{144+1440}}{4} \cr\cr x_1 &=& \dfrac{12}{4}+\dfrac{12\sqrt{11}}{4} = 3+3\sqrt{11} \cr\cr x_2 &=& \dfrac{12}{4}-\dfrac{12\sqrt{11}}{4} = 3-3\sqrt{11} \cr \cr \mathbb{L} &=& \{3-3\sqrt{11}; 3+3\sqrt{11}\} \end{array}