Beispiel Nr: 35
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{1}{8}x^2+\frac{1}{4}x+7\frac{7}{8} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{1}{8}x^{2}+\frac{1}{4}x+7\frac{7}{8} =0 \\ x_{1/2}=\displaystyle\frac{-\frac{1}{4} \pm\sqrt{\left(\frac{1}{4}\right)^{2}-4\cdot \left(-\frac{1}{8}\right) \cdot 7\frac{7}{8}}}{2\cdot\left(-\frac{1}{8}\right)} \\ x_{1/2}=\displaystyle \frac{-\frac{1}{4} \pm\sqrt{4}}{-\frac{1}{4}} \\ x_{1/2}=\displaystyle \frac{-\frac{1}{4} \pm2}{-\frac{1}{4}} \\ x_{1}=\displaystyle \frac{-\frac{1}{4} +2}{-\frac{1}{4}} \qquad x_{2}=\displaystyle \frac{-\frac{1}{4} -2}{-\frac{1}{4}} \\ x_{1}=-7 \qquad x_{2}=9 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{1}{8}x^{2}+\frac{1}{4}x+7\frac{7}{8} =0 \qquad /:-\frac{1}{8} \\ x^{2}-2x-63 =0 \\ x_{1/2}=\displaystyle -\frac{-2}{2}\pm\sqrt{\left(\frac{\left(-2\right)}{2}\right)^2- \left(-63\right)} \\ x_{1/2}=\displaystyle 1\pm\sqrt{64} \\ x_{1/2}=\displaystyle 1\pm8 \\ x_{1}=9 \qquad x_{2}=-7 \end{array}\\ \end{array}$