$-2x²+4x+4=0$
$⇔-2(x²-2x-2)=0$
$⇔x²-2x-2=0$
$⇔(x²-2x+1)-3=0$
$⇔(x-1)²-(\sqrt[]{3})²=0$
$⇔(x-1-\sqrt[]{3}).(x-1+\sqrt[]{3})=0$
$⇔$\(\left[ \begin{array}{l}x-1-√3=0\\x-1+\sqrt[]{3} =0\end{array} \right.\)
$⇔$\(\left[ \begin{array}{l}x=1+√3\\x=1-\sqrt[]{3}\end{array} \right.\)