\(1)3x^2-2x=0\\ \Leftrightarrow x\left(3x-2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\3x-2=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{2}{3}\end{matrix}\right.\)
\(2)2x^2-10=0\\ \Leftrightarrow2x^2=10\\ \Leftrightarrow x^2=5\\ \Leftrightarrow\left[{}\begin{matrix}x=-\sqrt{5}\\x=\sqrt{5}\end{matrix}\right.\)
\(3)x^2-49=0\\ \Leftrightarrow x^2=49\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\x=-7\end{matrix}\right.\)
\(4)x^2-7x+6=0\\ \Leftrightarrow x^2-x-6x+6=0\\ \Leftrightarrow x\left(x-1\right)-6\left(x-1\right)=0\\ \Leftrightarrow\left(x-1\right)\left(x-6\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-1=0\\x-6=0\end{matrix}\right.\\ \Leftrightarrow\left[{}\begin{matrix}x=1\\x=6\end{matrix}\right.\)