Hier noch einige Beispiele für quadratische Gleichungen:
$${\mathtt{\,-\,}}{\mathtt{3}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}} = {\mathtt{0}} = \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{4}}\\
{\mathtt{x}} = -{\mathtt{1}}\\
\end{array} \right\}$$
$${\mathtt{0.5}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,-\,}}{\mathtt{8.5}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,\small\textbf+\,}}{\mathtt{36}} = {\mathtt{0}} = \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{9}}\\
{\mathtt{x}} = {\mathtt{8}}\\
\end{array} \right\}$$
Und hier die ausführliche Lösung der 2. Gleichung:
1.) mit 2 multiplizieren: ergibt x^2-17x+72=0
2.) p-q-Formel anwenden: x1/2 = -p/2 +- sqrt( (p/2)^2 -q)
x1/2 = 8,5 +- sqrt(72,25 - 72)
x1/2 = 8,5 +- 0,5 x1 = 9 x2 = 8
Fleißig üben! Gruß Dieter ("radix")