Beispiel Nr: 24
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ x^2+6x-2 =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l} \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 1x^{2}+6x-2 =0 \\ x_{1/2}=\displaystyle\frac{-6 \pm\sqrt{6^{2}-4\cdot 1 \cdot \left(-2\right)}}{2\cdot1} \\ x_{1/2}=\displaystyle \frac{-6 \pm\sqrt{44}}{2} \\ x_{1/2}=\displaystyle \frac{-6 \pm6,63}{2} \\ x_{1}=\displaystyle \frac{-6 +6,63}{2} \qquad x_{2}=\displaystyle \frac{-6 -6,63}{2} \\ x_{1}=0,317 \qquad x_{2}=-6,32 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ \\ x^{2}+6x-2 =0 \\ x_{1/2}=\displaystyle -\frac{6}{2}\pm\sqrt{\left(\frac{6}{2}\right)^2- \left(-2\right)} \\ x_{1/2}=\displaystyle -3\pm\sqrt{11} \\ x_{1/2}=\displaystyle -3\pm3,32 \\ x_{1}=0,317 \qquad x_{2}=-6,32 \end{array}\\ \end{array}$