Beispiel Nr: 12
$ \text{Gegeben:} ax^{2}+bx+c=0 \\ \text{Gesucht:} \\ \text{Lösung der Gleichung} \\ \\ ax^{2}+bx+c=0 \\ \textbf{Gegeben:} \\ 2x^2-5x =0 \\ \\ \textbf{Rechnung:} \\ \begin{array}{l|l|l|l} \begin{array}{l} \text{x-Ausklammern}\\ \hline 2x^{2}-5x =0 \\ x(2x -5)=0 \\ \\ 2 x-5 =0 \qquad /+5 \\ 2 x= 5 \qquad /:2 \\ x=\displaystyle\frac{5}{2}\\ x_1=0\\ x_2=2\frac{1}{2} \end{array}& \begin{array}{l} \text{a-b-c Formel}\\ \hline \\ 2x^{2}-5x+0 =0 \\ x_{1/2}=\displaystyle\frac{+5 \pm\sqrt{\left(-5\right)^{2}-4\cdot 2 \cdot 0}}{2\cdot2} \\ x_{1/2}=\displaystyle \frac{+5 \pm\sqrt{25}}{4} \\ x_{1/2}=\displaystyle \frac{5 \pm5}{4} \\ x_{1}=\displaystyle \frac{5 +5}{4} \qquad x_{2}=\displaystyle \frac{5 -5}{4} \\ x_{1}=2\frac{1}{2} \qquad x_{2}=0 \end{array}& \begin{array}{l} \text{p-q Formel}\\ \hline \\ 2x^{2}-5x+0 =0 \qquad /:2 \\ x^{2}-2\frac{1}{2}x+0 =0 \\ x_{1/2}=\displaystyle -\frac{-2\frac{1}{2}}{2}\pm\sqrt{\left(\frac{\left(-2\frac{1}{2}\right)}{2}\right)^2- 0} \\ x_{1/2}=\displaystyle 1\frac{1}{4}\pm\sqrt{1\frac{9}{16}} \\ x_{1/2}=\displaystyle 1\frac{1}{4}\pm1\frac{1}{4} \\ x_{1}=2\frac{1}{2} \qquad x_{2}=0 \end{array}\\ \end{array}$