Beispiel Nr: 34
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{9}{25}x^2-2\frac{22}{25}x+3\frac{6}{25} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{9}{25}x^{2}-2\frac{22}{25}x+3\frac{6}{25} =0 \\ x_{1/2}=\displaystyle\frac{+2\frac{22}{25} \pm\sqrt{\left(-2\frac{22}{25}\right)^{2}-4\cdot \left(-\frac{9}{25}\right) \cdot 3\frac{6}{25}}}{2\cdot\left(-\frac{9}{25}\right)} \\ x_{1/2}=\displaystyle \frac{+2\frac{22}{25} \pm\sqrt{12\frac{24}{25}}}{-\frac{18}{25}} \\ x_{1/2}=\displaystyle \frac{2\frac{22}{25} \pm3\frac{3}{5}}{-\frac{18}{25}} \\ x_{1}=\displaystyle \frac{2\frac{22}{25} +3\frac{3}{5}}{-\frac{18}{25}} \qquad x_{2}=\displaystyle \frac{2\frac{22}{25} -3\frac{3}{5}}{-\frac{18}{25}} \\ x_{1}=-9 \qquad x_{2}=1 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{9}{25}x^{2}-2\frac{22}{25}x+3\frac{6}{25} =0 \qquad /:-\frac{9}{25} \\ x^{2}+8x-9 =0 \\ x_{1/2}=\displaystyle -\frac{8}{2}\pm\sqrt{\left(\frac{8}{2}\right)^2- \left(-9\right)} \\ x_{1/2}=\displaystyle -4\pm\sqrt{25} \\ x_{1/2}=\displaystyle -4\pm5 \\ x_{1}=1 \qquad x_{2}=-9 \end{array}\\ \end{array}$