\(2x^2-6x+7=0\)
\(\Leftrightarrow\left(x-1\right)^2+\left(x-2\right)^2+2=0\)
Ta có: \(\left(x-1\right)^2+\left(x-2\right)^2\ge0\forall x\)
\(\Rightarrow\left(x-1\right)^2+\left(x-2\right)^2+2\ge2\forall x\)
\(\Rightarrow\) Phương trình vô nghiệm.