Aloha :)
$$\left.-6e^{3x}+2xe^{3x}+3x^2e^{3x}=0\quad\right|\quad\text{\(e^{3x}\) ausklammern}$$$$\left.e^{3x}(-6+2x+3x^2)=0\quad\right|\quad\text{Da \(e^{3x}>0\) für alle \(x\in\mathbb R\) dividieren durch \(e^{3x}\)}$$$$\left.3x^2+2x-6=0\quad\right|\quad\div3$$$$\left.x^2+\frac{2}{3}x-2=0\quad\right|\quad\text{pq-Formel}$$$$x_{1,2}=-\frac{1}{3}\pm\sqrt{\frac{1}{9}+2}=-\frac{1}{3}\pm\sqrt{\frac{19}{9}}=\frac{-1\pm\sqrt{19}}{3}$$
