Here $DE\parallel AC$

From the figure

$\frac{BE}{BC}=\frac{DE}{AC}$

$\Rightarrow \frac{6}{6+x}=\frac{x-1}{2x+4}$

$\Rightarrow 6(2x+4)=(6+x)(x-1)$

$\Rightarrow 12x+24=6x-6+{x}^{2}-x$

$\Rightarrow 12x+24=5x+{x}^{2}-6$

$\Rightarrow {x}^{2}+5x-6-12x-24=0$

$\Rightarrow {x}^{2}-7x-30=0$

$\Rightarrow {x}^{2}-10x+3x-30=0$

$\Rightarrow x(x-10)+3(x-10)=0$

$\Rightarrow (x-10)(x+3)=0$

$\Rightarrow$ either x-10=0 or, x+3=0

$\Rightarrow x=10\Rightarrow x=-3$

x=-3 is not possitive since length is non negative

Hence x=10