Beispiel Nr: 32
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ 12x^2+12x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline 12x^{2}+12x =0 \\ x(12x +12)=0 \\ \\ 12 x+12 =0 \qquad /-12 \\ 12 x= -12 \qquad /:12 \\ x=\displaystyle\frac{-12}{12}\\ x_1=0\\ x_2=-1 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 12x^{2}+12x+0 =0 \\ x_{1/2}=\displaystyle\frac{-12 \pm\sqrt{12^{2}-4\cdot 12 \cdot 0}}{2\cdot12} \\ x_{1/2}=\displaystyle \frac{-12 \pm\sqrt{144}}{24} \\ x_{1/2}=\displaystyle \frac{-12 \pm12}{24} \\ x_{1}=\displaystyle \frac{-12 +12}{24} \qquad x_{2}=\displaystyle \frac{-12 -12}{24} \\ x_{1}=0 \qquad x_{2}=-1 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ 12x^{2}+12x+0 =0 \qquad /:12 \\ x^{2}+1x+0 =0 \\ x_{1/2}=\displaystyle -\frac{1}{2}\pm\sqrt{\left(\frac{1}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle -\frac{1}{2}\pm\sqrt{\frac{1}{4}} \\ x_{1/2}=\displaystyle -\frac{1}{2}\pm\frac{1}{2} \\ x_{1}=0 \qquad x_{2}=-1 \end{array}\\ \end{array}$