Solve each of the following quadratic equations:

We write, $7 x=5 x+2 x$ as $\sqrt{2} x^{2} \times 5 \sqrt{2}=10 x^{2}=5 x \times 2 x$

$\therefore \sqrt{2} x^{2}+7 x+5 \sqrt{2}=0$

$\Rightarrow \sqrt{2} x^{2}+5 x+2 x+5 \sqrt{2}=0$

$\Rightarrow x(\sqrt{2} x+5)+\sqrt{2}(\sqrt{2} x+5)=0$

$\Rightarrow(\sqrt{2} x+5)(x+\sqrt{2})=0$

$\Rightarrow x+\sqrt{2}=0$ or $\sqrt{2} x+5=0$

$\Rightarrow x=-\sqrt{2}$ or $x=-\frac{5}{\sqrt{2}}=-\frac{5 \sqrt{2}}{2}$

Hence, the roots of the given equation are $-\sqrt{2}$ and $-\frac{5 \sqrt{2}}{2}$.