TeX Quellcode:

\begin{array}{rclcl} 5x^2-\left(\sqrt{175}-15\right)x &=& \dfrac{15}{2}\sqrt{7} &\vert& -\dfrac{15}{2}\sqrt{7} \cr\cr 5x^2-\left(\sqrt{25\cdot 7}-15\right)x-\dfrac{15}{2}\sqrt{7} &=& 0 &\vert& :5 \cr\cr x^2-\dfrac{1}{5}\left(5\left(\sqrt{7}-3\right)\right)x-\dfrac{3}{2}\sqrt{7} &=& 0 \cr\cr x^2-\left(\sqrt{7}-3\right)x-\dfrac{3}{2}\sqrt{7} &=& 0 \cr\cr x_{1,2} &=& \dfrac{\sqrt{7}-3}{2} \pm \sqrt{\left(\dfrac{\sqrt{7}-3}{2}\right)^2 -\left(-\dfrac{3}{2}\sqrt{7}\right)} \cr\cr &=& \dfrac{\sqrt{7}-3}{2} \pm \sqrt{\dfrac{7-6\sqrt{7}+9}{4} +\dfrac{6}{4}\sqrt{7}} \cr\cr &=& \dfrac{\sqrt{7}-3}{2} \pm \sqrt{\dfrac{16}{4}} \cr\cr &=& \dfrac{\sqrt{7}-3}{2} \pm \sqrt{4} \cr\cr &=& \dfrac{\sqrt{7}-3}{2} \pm 2 \cr\cr\cr x_1 &=& \dfrac{\sqrt{7}}{2}-\dfrac{3}{2}+2 = \dfrac{\sqrt{7}}{2}+\dfrac{1}{2} \cr\cr x_2 &=& \dfrac{\sqrt{7}}{2}-\dfrac{3}{2}-2 = \dfrac{\sqrt{7}}{2}-\dfrac{7}{2} \cr \cr \mathbb{L} &=& \left\{\dfrac{\sqrt{7}}{2}-\dfrac{7}{2}; \dfrac{\sqrt{7}}{2}+\dfrac{1}{2} \right\} \end{array}