TeX Quellcode:

\begin{array}{rclcl} -\dfrac{12}{27}x^2 &=& \dfrac{1}{9}\left(\dfrac{1}{3}\left(15x^2-\dfrac{2}{3}\right)-\dfrac{7}{2}x\right) \cr\cr -\dfrac{12}{27}x^2 &=& \dfrac{1}{27}\left(15x^2-\dfrac{2}{3}\right)-\dfrac{7}{18}x \cr\cr -\dfrac{12}{27}x^2 &=& \dfrac{15}{27}x^2-\dfrac{2}{81}-\dfrac{7}{18}x &\vert& +\dfrac{12}{27}x^2 \cr\cr 0 &=& x^2-\dfrac{7}{18}x-\dfrac{2}{81} \cr\cr x_{1,2} &=& \dfrac{7}{36} \pm \sqrt{\dfrac{49}{1.296}+\dfrac{2}{81}} \cr\cr x_1 &=& \dfrac{7}{36}+\dfrac{1}{4} = \dfrac{4}{9} \cr\cr x_2 &=& \dfrac{7}{36}-\dfrac{1}{4} = -\dfrac{1}{18} \cr \cr \mathbb{L} &=& \left\{-\dfrac{1}{18};\dfrac{4}{9}\right\} \end{array}