\(S_n=\frac{n\left(u_1+u_n\right)}{2}=2n^2-3n\Rightarrow u_1+u_n=4n-6\) \(\forall n\)
\(\Rightarrow2u_1+\left(n-1\right)d=4n-6\)
\(\Rightarrow n.d+2u_1-d=4n-6\)
\(\Rightarrow\left\{{}\begin{matrix}d=4\\2u_1-d=-6\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}d=4\\u_1=-1\end{matrix}\right.\)