Beispiel Nr: 36
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ \frac{20}{49}x^2+3\frac{33}{49}x+3\frac{13}{49} =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ \frac{20}{49}x^{2}+3\frac{33}{49}x+3\frac{13}{49} =0 \\ x_{1/2}=\displaystyle\frac{-3\frac{33}{49} \pm\sqrt{\left(3\frac{33}{49}\right)^{2}-4\cdot \frac{20}{49} \cdot 3\frac{13}{49}}}{2\cdot\frac{20}{49}} \\ x_{1/2}=\displaystyle \frac{-3\frac{33}{49} \pm\sqrt{8\frac{8}{49}}}{\frac{40}{49}} \\ x_{1/2}=\displaystyle \frac{-3\frac{33}{49} \pm2\frac{6}{7}}{\frac{40}{49}} \\ x_{1}=\displaystyle \frac{-3\frac{33}{49} +2\frac{6}{7}}{\frac{40}{49}} \qquad x_{2}=\displaystyle \frac{-3\frac{33}{49} -2\frac{6}{7}}{\frac{40}{49}} \\ x_{1}=-1 \qquad x_{2}=-8 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \frac{20}{49}x^{2}+3\frac{33}{49}x+3\frac{13}{49} =0 \qquad /:\frac{20}{49} \\ x^{2}+9x+8 =0 \\ x_{1/2}=\displaystyle -\frac{9}{2}\pm\sqrt{\left(\frac{9}{2}\right)^2- 8} \\ x_{1/2}=\displaystyle -4\frac{1}{2}\pm\sqrt{12\frac{1}{4}} \\ x_{1/2}=\displaystyle -4\frac{1}{2}\pm3\frac{1}{2} \\ x_{1}=-1 \qquad x_{2}=-8 \end{array}\\ \end{array}$