Beispiel Nr: 33
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{6}{25}x^2+1\frac{23}{25}x+2\frac{4}{25} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{6}{25}x^{2}+1\frac{23}{25}x+2\frac{4}{25} =0 \\ x_{1/2}=\displaystyle\frac{-1\frac{23}{25} \pm\sqrt{\left(1\frac{23}{25}\right)^{2}-4\cdot \left(-\frac{6}{25}\right) \cdot 2\frac{4}{25}}}{2\cdot\left(-\frac{6}{25}\right)} \\ x_{1/2}=\displaystyle \frac{-1\frac{23}{25} \pm\sqrt{5\frac{19}{25}}}{-\frac{12}{25}} \\ x_{1/2}=\displaystyle \frac{-1\frac{23}{25} \pm2\frac{2}{5}}{-\frac{12}{25}} \\ x_{1}=\displaystyle \frac{-1\frac{23}{25} +2\frac{2}{5}}{-\frac{12}{25}} \qquad x_{2}=\displaystyle \frac{-1\frac{23}{25} -2\frac{2}{5}}{-\frac{12}{25}} \\ x_{1}=-1 \qquad x_{2}=9 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{6}{25}x^{2}+1\frac{23}{25}x+2\frac{4}{25} =0 \qquad /:-\frac{6}{25} \\ x^{2}-8x-9 =0 \\ x_{1/2}=\displaystyle -\frac{-8}{2}\pm\sqrt{\left(\frac{\left(-8\right)}{2}\right)^2- \left(-9\right)} \\ x_{1/2}=\displaystyle 4\pm\sqrt{25} \\ x_{1/2}=\displaystyle 4\pm5 \\ x_{1}=9 \qquad x_{2}=-1 \end{array}\\ \end{array}$