The term in \(x\) from \(\left(1 + \frac{x}{2}\right)^n\) is \(\frac{nx}{2}\).

In the expansion of \((3 - 2x)(1 + \frac{nx}{2} + \ldots)\), the coefficient of \(x\) is given by:

\(3 \cdot \frac{nx}{2} - 2 = 7\)

\(\frac{3n}{2} - 2 = 7\)

\(\frac{3n}{2} = 9\)

\(n = 6\)

Now, find the coefficient of \(x^2\):

The term in \(x^2\) from \(\left(1 + \frac{x}{2}\right)^n\) is \(\frac{n(n-1)}{2} \left(\frac{x}{2}\right)^2\).

The coefficient of \(x^2\) is:

\(\frac{3n(n-1)}{8} - \frac{2n}{2}\)

Substitute \(n = 6\):

\(\frac{3 \times 6 \times 5}{8} - 6 = \frac{90}{8} - 6 = \frac{45}{4} - 6 = \frac{21}{4}\)