Let \(u = x^{\frac{1}{2}}\), then \(u^2 = x\).

The equation becomes:

\(4u^2 - 11u + 6 = 0\)

Factor the quadratic equation:

\((4u - 3)(u - 2) = 0\)

Set each factor to zero:

\(4u - 3 = 0 \quad \text{or} \quad u - 2 = 0\)

Solve for \(u\):

\(u = \frac{3}{4} \quad \text{or} \quad u = 2\)

Since \(u = x^{\frac{1}{2}}\), square both sides to find \(x\):

\(x = \left(\frac{3}{4}\right)^2 = \frac{9}{16} \quad \text{or} \quad x = 2^2 = 4\)

Thus, the solutions are \(x = \frac{9}{16}\) or \(x = 4\).