\[Уравнение\ имеет\ \]
\[единственный\ корень\ \]
\[при\ D = 0.\]
\[(c - 6)x^{2} + (c - 4)x + 2 = 0\]
\[D = (c - 4)^{2} - 4 \cdot (c - 6) \cdot 2 =\]
\[= c^{2} - 8c + 16 - 8c + 48 =\]
\[= c^{2} - 16c + 64 = (c - 8)^{2}\]
\[(c - 8)^{2} = 0\]
\[c - 8 = 0\]
\[c = 8.\]
\[c - 6 = 0\ \ \]
\[c = 6.\]
\[Ответ:\ \ при\ c = 8;\ c = 6.\]