\(3x-\sqrt{4x^2-4x+1}=0\)
\(\Leftrightarrow3x-\sqrt{\left(2x-1\right)^2}=0\)
\(\Leftrightarrow3x=\sqrt{\left(2x-1\right)^2}\)
\(\Leftrightarrow3x=\left|2x-1\right|\)
\(\Leftrightarrow\left[{}\begin{matrix}-3x=2x-1\left(ĐK:x< \dfrac{1}{2}\right)\\3x=2x-1\left(ĐK:x\ge\dfrac{1}{2}\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}2x+3x=1\\3x-2x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}5x=1\\x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{5}\left(tm\right)\\x=-1\left(ktm\right)\end{matrix}\right.\)
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