Solve each of the following quadratic equations:

We write, $13 x=5 x+8 x$ as $5 x^{2} \times 8=40 x^{2}=5 x \times 8 x$

$\therefore 5 x^{2}+13 x+8=0$

$\Rightarrow 5 x^{2}+5 x+8 x+8=0$

$\Rightarrow 5 x(x+1)+8(x+1)=0$

$\Rightarrow(x+1)(5 x+8)=0$

$\Rightarrow x+1=0$ or $5 x+8=0$

$\Rightarrow x=-1$ or $x=-\frac{8}{5}$

Hence, $-1$ and $-\frac{8}{5}$ are the roots of the given equation.