\(\left(3x^2-x+1\right)\left(x-1\right)+x^2\left(4-3x\right)=\dfrac{5}{2}\\ \Leftrightarrow\left(3x^2-x+1\right).x-\left(3x^2-x+1\right)+4x^2-3x^3=\dfrac{5}{2}\\ \Leftrightarrow3x^3-x^2+x-3x^2+x-1+4x^2-3x^3=\dfrac{5}{2}\)
\(\Leftrightarrow2x-1=\dfrac{5}{2}\\ \Leftrightarrow2x=\dfrac{7}{2}\\ \Leftrightarrow x=\dfrac{7}{4}\)