Beispiel Nr: 09
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -2x^2-8x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline -2x^{2}-8x =0 \\ x(-2x -8)=0 \\ \\ -2 x-8 =0 \qquad /+8 \\ -2 x= 8 \qquad /:\left(-2\right) \\ x=\displaystyle\frac{8}{-2}\\ x_1=0\\ x_2=-4 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -2x^{2}-8x+0 =0 \\ x_{1/2}=\displaystyle\frac{+8 \pm\sqrt{\left(-8\right)^{2}-4\cdot \left(-2\right) \cdot 0}}{2\cdot\left(-2\right)} \\ x_{1/2}=\displaystyle \frac{+8 \pm\sqrt{64}}{-4} \\ x_{1/2}=\displaystyle \frac{8 \pm8}{-4} \\ x_{1}=\displaystyle \frac{8 +8}{-4} \qquad x_{2}=\displaystyle \frac{8 -8}{-4} \\ x_{1}=-4 \qquad x_{2}=0 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -2x^{2}-8x+0 =0 \qquad /:-2 \\ x^{2}+4x+0 =0 \\ x_{1/2}=\displaystyle -\frac{4}{2}\pm\sqrt{\left(\frac{4}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle -2\pm\sqrt{4} \\ x_{1/2}=\displaystyle -2\pm2 \\ x_{1}=0 \qquad x_{2}=-4 \end{array}\\ \end{array}$