Beispiel Nr: 21
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ 2x^2+4x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline 2x^{2}+4x =0 \\ x(2x +4)=0 \\ \\ 2 x+4 =0 \qquad /-4 \\ 2 x= -4 \qquad /:2 \\ x=\displaystyle\frac{-4}{2}\\ x_1=0\\ x_2=-2 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 2x^{2}+4x+0 =0 \\ x_{1/2}=\displaystyle\frac{-4 \pm\sqrt{4^{2}-4\cdot 2 \cdot 0}}{2\cdot2} \\ x_{1/2}=\displaystyle \frac{-4 \pm\sqrt{16}}{4} \\ x_{1/2}=\displaystyle \frac{-4 \pm4}{4} \\ x_{1}=\displaystyle \frac{-4 +4}{4} \qquad x_{2}=\displaystyle \frac{-4 -4}{4} \\ x_{1}=0 \qquad x_{2}=-2 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ 2x^{2}+4x+0 =0 \qquad /:2 \\ x^{2}+2x+0 =0 \\ x_{1/2}=\displaystyle -\frac{2}{2}\pm\sqrt{\left(\frac{2}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle -1\pm\sqrt{1} \\ x_{1/2}=\displaystyle -1\pm1 \\ x_{1}=0 \qquad x_{2}=-2 \end{array}\\ \end{array}$