Beispiel Nr: 30
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ -\frac{3}{4}x^2-3x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline -\frac{3}{4}x^{2}-3x =0 \\ x(-\frac{3}{4}x -3)=0 \\ \\ -\frac{3}{4} x-3 =0 \qquad /+3 \\ -\frac{3}{4} x= 3 \qquad /:\left(-\frac{3}{4}\right) \\ x=\displaystyle\frac{3}{-\frac{3}{4}}\\ x_1=0\\ x_2=-4 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ -\frac{3}{4}x^{2}-3x+0 =0 \\ x_{1/2}=\displaystyle\frac{+3 \pm\sqrt{\left(-3\right)^{2}-4\cdot \left(-\frac{3}{4}\right) \cdot 0}}{2\cdot\left(-\frac{3}{4}\right)} \\ x_{1/2}=\displaystyle \frac{+3 \pm\sqrt{9}}{-1\frac{1}{2}} \\ x_{1/2}=\displaystyle \frac{3 \pm3}{-1\frac{1}{2}} \\ x_{1}=\displaystyle \frac{3 +3}{-1\frac{1}{2}} \qquad x_{2}=\displaystyle \frac{3 -3}{-1\frac{1}{2}} \\ x_{1}=-4 \qquad x_{2}=0 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ -\frac{3}{4}x^{2}-3x+0 =0 \qquad /:-\frac{3}{4} \\ x^{2}+4x+0 =0 \\ x_{1/2}=\displaystyle -\frac{4}{2}\pm\sqrt{\left(\frac{4}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle -2\pm\sqrt{4} \\ x_{1/2}=\displaystyle -2\pm2 \\ x_{1}=0 \qquad x_{2}=-4 \end{array}\\ \end{array}$