Solve each of the following quadratic equations:

$\frac{1}{2 a+b+2 x}=\frac{1}{2 a}+\frac{1}{b}+\frac{1}{2 x}$

$\Rightarrow \frac{1}{2 a+b+2 x}-\frac{1}{2 x}=\frac{1}{2 a}+\frac{1}{b}$

$\Rightarrow \frac{2 x-2 a-b-2 x}{2 x(2 a+b+2 x)}=\frac{2 a+b}{2 a b}$

$\Rightarrow \frac{-(2 a+b)}{4 x^{2}+4 a x+2 b x}=\frac{2 a+b}{2 a b}$

$\Rightarrow 4 x^{2}+4 a x+2 b x=-2 a b$

$\Rightarrow 4 x^{2}+4 a x+2 b x+2 a b=0$

$\Rightarrow 4 x(x+a)+2 b(x+a)=0$

$\Rightarrow(x+a)(4 x+2 b)=0$

$\Rightarrow x+a=0$ or $4 x+2 b=0$

$\Rightarrow x=-a$ or $x=-\frac{b}{2}$

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