\(-x^2+16x+6=0\)
\(\Leftrightarrow x^2-16x-6=0\)
\(\Leftrightarrow\left(x^2-16x+64\right)-70=0\)
\(\Leftrightarrow\left(x-8\right)^2=70\)
\(\Leftrightarrow x-8=\pm\sqrt{70}\)
\(\Leftrightarrow x=\pm\sqrt{70}+8\)
Vậy \(S=\left\{8+\sqrt{70};8-\sqrt{70}\right\}\)