TeX Quellcode:

\begin{array}{rclcl} 3x-19x^2 &=& -18x^2+\dfrac{10}{4} &\vert& -3x + 19x^2 \cr\cr 0 &=& x^2 -3x+ \dfrac{10}{4} &\vert& \text{p-q-Formel} \cr\cr x_{1,2} &=& \dfrac{3}{2} \pm \sqrt{\left(\dfrac{-3}{2}\right)^2 -\dfrac{10}{4}} \cr\cr &=& \dfrac{3}{2} \pm \sqrt{-\dfrac{1}{4}} \cr\cr &=& \dfrac{3}{2} \pm \sqrt{-1\cdot\dfrac{1}{4}} \cr\cr &=& \dfrac{3}{2} \pm \dfrac{1}{2} \sqrt{-1} &\vert& \sqrt{-1}=i \cr\cr\cr x_1 &=& \dfrac{3}{2}+\dfrac{1}{2}i \cr\cr x_2 &=& \dfrac{3}{2}-\dfrac{1}{2}i \cr \cr\cr \mathbb{L} &=& \left\{ \dfrac{3}{2}+\dfrac{1}{2}i \; ; \; \dfrac{3}{2}-\dfrac{1}{2}i\right\} \end{array}