To find the equation of the curve, we need to integrate \(\frac{dy}{dx} = \frac{8}{(5 - 2x)^2}\).

Let \(f(x) = \int \frac{8}{(5 - 2x)^2} \, dx\).

Using substitution, let \(u = 5 - 2x\), then \(\frac{du}{dx} = -2\) or \(dx = -\frac{1}{2} \, du\).

Substitute into the integral:

\(f(x) = \int \frac{8}{u^2} \left(-\frac{1}{2}\right) \, du = -4 \int u^{-2} \, du\).

Integrate: \(f(x) = -4 \left( \frac{u^{-1}}{-1} \right) + c = \frac{4}{u} + c\).

Substitute back \(u = 5 - 2x\):

\(f(x) = \frac{4}{5 - 2x} + c\).

Given the curve passes through (2, 7), substitute \(x = 2\) and \(y = 7\):

\(7 = \frac{4}{5 - 2(2)} + c\).

\(7 = \frac{4}{1} + c\).

\(7 = 4 + c\).

\(c = 3\).

Thus, the equation of the curve is \(y = \frac{4}{5 - 2x} + 3\).