$$x^{2}-2x+a=0; (x_{1}-x_{2})=16$$
$x=\sqrt{1-a}+1$
$x=-\sqrt{1-a}+1\text{, }x_{1}=x_{2}+16$
$x=\sqrt{1-a}+1$
$x=-\sqrt{1-a}+1\text{, }a\leq 1\text{ and }x_{1}=x_{2}+16$
