\(x\left(2x-1\right)+\frac{1}{3}-\frac{2}{3}x=0\)
\(2x^2-x+\frac{1}{3}-\frac{2}{3}x=0\)
\(2x^2-\frac{5}{3}x+\frac{1}{3}=0\)
\(6x^2-5x+1=0\)
\(6x^2-3x-2x+1\)
\(3x\left(2x-1\right)-\left(2x-1\right)=0\)
\(\left(3x-1\right)\left(2x-1\right)=0\)
\(\orbr{\begin{cases}x=\frac{1}{3}\\x=\frac{1}{2}\end{cases}}\)