2. For real numbers $a, b, c$ and a positive number $\lambda$, such that
$$
f(x)=x^{3}+a x^{2}+b x+c
$$

has three real roots $x_{1}, x_{2}, x_{3}$, and satisfies:
(1) $x_{2}-x_{1}=\lambda$;
(2) $x_{3}>\frac{1}{2}\left(x_{1}+x_{2}\right)$.
Find the maximum value of $\frac{2 a^{3}+27 c-9 a b}{\lambda^{3}}$.
(Let $x_{2}=x_{1}+2 m, x_{3}=x_{1}+m+n(m>0$, $n>0, \lambda=2 m)$, then $2 a^{3}+27 c-9 a b=2 n\left(9 m^{2}-n^{2}\right)$. Let $t=\frac{n}{m}$, substitute it in. By the AM-GM inequality, the maximum value is $\frac{3 \sqrt{3}}{2}$.)