TeX Quellcode:

\begin{array}{crclcl}& \mathbb{D} &=& \mathbb{R} \\\\& 3\left(\dfrac{1}{3} x^2-112\right) e^{2x+6} &=& -\dfrac{109x}{e^{-2x-6}} \\\\& \left(x^2-336\right) e^{2x+6} &=& -109x\cdot e^{-(-2x-6)} &\vert& +109xe^{2x+6}\\\\& \left(x^2-336\right) e^{2x+6} +109xe^{2x+6} &=& 0\\\\& \left(x^2+109x-336\right) e^{2x+6} &=& 0 &\vert& \text{Satz vom Nullprodukt} \\\\\text{Faktor 1:} & x^2+109x-336 &=& 0 &\vert & \text{p-q-Formel} \\\\& x_{1,2} &=& -\dfrac{109}{2}\pm \sqrt{\left(\dfrac{109}{2}\right)^2+336} \\\\& x_{1,2} &=& -\dfrac{109}{2}\pm \sqrt{\dfrac{13.225}{4}} \\\\& x_{1} &=& -\dfrac{109}{2}+\dfrac{115}{2} = 3 \\\\& x_{2} &=& -\dfrac{109}{2}-\dfrac{115}{2} = -112 \\\\\\\text{Faktor 2:} & e^{2x+6} &=& 0\end{array}