TeX Quellcode:

\begin{array}{rclcl} 5\sqrt{-1+x}+80 &=& 5x+15 &\vert& -80 \cr 5\sqrt{-1+x} &=& 5x-65 &\vert& :5 \cr \sqrt{-1+x} &=& x-13 &\vert& ()^2 \cr -1+x &=& (x-13)^2 \cr -1+x &=& x^2-26x+169 &\vert& +1-x \cr 0 &=& x^2-27x+170 &\vert& \text{p-q-Formel} \cr x_{1,2} &=& \dfrac{27}{2} \pm \sqrt{\left(-\dfrac{27}{2}\right)^2-170} \cr x_{1,2} &=& \dfrac{27}{2} \pm \sqrt{\dfrac{49}{4}} \cr\cr x_1 &=& \dfrac{27}{2} + \dfrac{7}{2} = 17\;\in\;\mathbb{D} \cr x_2 &=& \dfrac{27}{2} - \dfrac{7}{2} = 10\;\in\;\mathbb{D} \end{array}