TeX Quellcode:

\begin{array}{lrclll}& \mathbb{D} &=& \mathbb{R} \\\\& 3e^{-\frac{2}{3}y+5}\cdot\left(y^3+3y^2-4y\right) &=& 0 \\\\\text{Faktor 1:} & 3e^{-\frac{2}{3}y+5} &= & 0 &\vert& :3 \\& e^{-\frac{2}{3}y+5} &= & 0 \\\\\text{Faktor 2:} & y^3+3y^2-4y &=& 0 \\& y\left(y^2+3y-4\right) &=& 0 \\\text{Faktor 2.1:} & y_1 &=& 0 \\\\\text{Faktor 2.2:} & y^2+3y-4 &=& 0 &\vert& \text{p-q-Formel} \\& y_{2,3} &=& -\dfrac{3}{2}\pm\sqrt{\left(\dfrac{3}{2}\right)^2+4}\\& y_{2,3} &=& -\dfrac{3}{2}\pm\sqrt{\dfrac{25}{4}}\\\\& y_2 &=& -\dfrac{3}{2}+\dfrac{5}{2} = 1\\& y_3 &=& -\dfrac{3}{2}-\dfrac{5}{2} = -4\end{array}