\ANG{
L"ose die Gleichung mit quadratischer Erg"anzung:\qquad$8x^{2}+2x-3=0$
}
\LSG{
\begin{align}
8x^{2}+2x-3 &=0\,\,\, |:8 \nonumber\\
x^{2}+2\cdot\frac18\cdot x+\left(\frac18\right)^{2} &=\frac38+\frac{1}{64} \nonumber\\
\left(x+\frac18\right)^{2} &=\frac{25}{64} \nonumber\\
x &=-\frac18\pm\frac{5}{8} \nonumber
\end{align}
\[x_{1}=\frac12,\quad x_{2}=-\frac34,\quad\LL=\left\{-\frac34,\frac12\right\}\]
}