Beispiel Nr: 43
$\text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ 4x^2-8x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline 4x^{2}-8x =0 \\ x(4x -8)=0 \\ \\ 4 x-8 =0 \qquad /+8 \\ 4 x= 8 \qquad /:4 \\ x=\displaystyle\frac{8}{4}\\ x_1=0\\ x_2=2 \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 4x^{2}-8x+0 =0 \\ x_{1/2}=\displaystyle\frac{+8 \pm\sqrt{\left(-8\right)^{2}-4\cdot 4 \cdot 0}}{2\cdot4} \\ x_{1/2}=\displaystyle \frac{+8 \pm\sqrt{64}}{8} \\ x_{1/2}=\displaystyle \frac{8 \pm8}{8} \\ x_{1}=\displaystyle \frac{8 +8}{8} \qquad x_{2}=\displaystyle \frac{8 -8}{8} \\ x_{1}=2 \qquad x_{2}=0 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ 4x^{2}-8x+0 =0 \qquad /:4 \\ x^{2}-2x+0 =0 \\ x_{1/2}=\displaystyle -\frac{-2}{2}\pm\sqrt{\left(\frac{\left(-2\right)}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle 1\pm\sqrt{1} \\ x_{1/2}=\displaystyle 1\pm1 \\ x_{1}=2 \qquad x_{2}=0 \end{array}\\ \end{array}$