First, find \(\frac{dy}{dx}\) for the curve \(y = x^2 - \frac{10}{3}x^{3/2} + 5x\).

\(\frac{dy}{dx} = 2x - 5x^{1/2} + 5\).

Given that \(\frac{dy}{dt} = 2\), we equate \(\frac{dy}{dx}\) to 2:

\(2x - 5x^{1/2} + 5 = 2\).

Simplify to get:

\(2x - 5x^{1/2} + 3 = 0\).

Factor the quadratic equation:

\((2x^{1/2} - 3)(x^{1/2} - 1) = 0\).

Solving gives:

\(x^{1/2} = \frac{3}{2}\) or \(x^{1/2} = 1\).

Thus, \(x = \frac{9}{4}\) and \(x = 1\).