%%0,5x^2-1,5x-14=0%%

%%0,5x^2-1,5x-14=0%%

%%0,5%% ausklammern.

%%0,5\left(x^2-3x\right)-14=0%%

%%0,5\left(x^2-3x+\left(\frac32\right)^2-\left(\frac32\right)^2\right)-14=0%%

Zur 2. binomischen Formel zusammenfassen.

%%0,5\left(\left(x-\frac32\right)^2-\frac94\right)-14=0%%

%%0,5\left(x-\frac32\right)^2-\frac98-14=0%%

Gleichung umformen.

%%\begin{array}{rclc}0,5\left(x-\frac32\right)^2-\frac98-14&=&0&\end{array}%%

%%\left|+14+\frac98\right.%%

%%\begin{array}{rcl}0,5\left(x-\frac32\right)^2&=&14+\frac98\end{array}%%

$$\left|\cdot2\right.$$

%%\begin{array}{rcl}\left(x-\frac32\right)^2&=&28+\frac94\end{array}%%

$$\left|\sqrt\;\right.$$

%%\begin{array}{rcl}x-\frac32&=&\pm\sqrt{\frac{121}4}\end{array}%%

%%\left|+\frac32\right.%%

%%\begin{array}{rcl}x&=&\frac32\pm\frac{11}2\end{array}%%

Lösungsmenge angeben.

%%L=\left\{-4;\;7\right\}%%