To solve the equation \(2\cos x - 1 = 0\), we first isolate the cosine term by adding 1 to both sides, giving:
$$2\cos x = 1$$
Next, we divide both sides by 2 to obtain:
$$\cos x = \frac{1}{2}$$
From the unit circle or trigonometric ratios, we know that the solutions to this equation are the angles whose cosine is equal to 1/2, which are \(\frac{\pi}{3}\) and \(\frac{5\pi}{3}\) (or their reference angles in the interval [0, 2π)). Therefore, the answer is \((\frac{\pi}{3}, \frac{5\pi}{3})\).