TeX Quellcode:

\begin{array}{rclcll}\dfrac{10x^2+4x}{16x-36x^2} &=& \dfrac{3}{x} \cr\cr \dfrac{2x(5x+2)}{2x(8-18x)} &=& \dfrac{3}{x} \cr\cr \dfrac{5x+2}{-18x+8} &=& \dfrac{3}{x} &\vert& \text{Kehrwert} \cr\cr \dfrac{-18x+8}{5x+2} &=& \dfrac{x}{3} & \vert & \cdot (5x+2)\cdot 3 \cr -54x+24 &=& 5x^2+2x & \vert & +54x-24 \cr 0 &=& 5x^2+56x-24 & \vert & :5 \cr 0 &=& x^2+\dfrac{56}{5}x-\dfrac{24}{5} &\vert& \text{p-q-Formel} \cr x_{1,2} &=& -\dfrac{28}{5} \pm \sqrt{\left(\dfrac{28}{5}\right)^2+\dfrac{24}{5}} \cr x_{1,2} &=& -\dfrac{28}{5} \pm \sqrt{\dfrac{904}{25}} \cr\cr x_1 &=& -\dfrac{28+\sqrt{904}}{5} \approx 0{,}41 \;\in\;\mathbb{D} \cr x_2 &=& -\dfrac{28-\sqrt{904}}{5} \approx -11{,}61 \;\in\;\mathbb{D}\end{array}