Beispiel Nr: 47
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ 1\frac{11}{25}x^2+10\frac{2}{25}x+8\frac{16}{25} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1\frac{11}{25}x^{2}+10\frac{2}{25}x+8\frac{16}{25} =0 \\ x_{1/2}=\displaystyle\frac{-10\frac{2}{25} \pm\sqrt{\left(10\frac{2}{25}\right)^{2}-4\cdot 1\frac{11}{25} \cdot 8\frac{16}{25}}}{2\cdot1\frac{11}{25}} \\ x_{1/2}=\displaystyle \frac{-10\frac{2}{25} \pm\sqrt{51\frac{21}{25}}}{2\frac{22}{25}} \\ x_{1/2}=\displaystyle \frac{-10\frac{2}{25} \pm7\frac{1}{5}}{2\frac{22}{25}} \\ x_{1}=\displaystyle \frac{-10\frac{2}{25} +7\frac{1}{5}}{2\frac{22}{25}} \qquad x_{2}=\displaystyle \frac{-10\frac{2}{25} -7\frac{1}{5}}{2\frac{22}{25}} \\ x_{1}=-1 \qquad x_{2}=-6 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ 1\frac{11}{25}x^{2}+10\frac{2}{25}x+8\frac{16}{25} =0 \qquad /:1\frac{11}{25} \\ x^{2}+7x+6 =0 \\ x_{1/2}=\displaystyle -\frac{7}{2}\pm\sqrt{\left(\frac{7}{2}\right)^2- 6} \\ x_{1/2}=\displaystyle -3\frac{1}{2}\pm\sqrt{6\frac{1}{4}} \\ x_{1/2}=\displaystyle -3\frac{1}{2}\pm2\frac{1}{2} \\ x_{1}=-1 \qquad x_{2}=-6 \end{array}\\ \end{array}$