(a) Let \(u = \sqrt{y}\). Then the equation becomes \(6u + \frac{2}{u} - 7 = 0\).

Multiply through by \(u\) to clear the fraction: \(6u^2 + 2 - 7u = 0\).

Rearrange to form a quadratic: \(6u^2 - 7u + 2 = 0\).

Factor the quadratic: \((2u - 1)(3u - 2) = 0\).

Thus, \(u = \frac{1}{2}\) or \(u = \frac{2}{3}\).

Since \(u = \sqrt{y}\), we have \(\sqrt{y} = \frac{1}{2}\) or \(\sqrt{y} = \frac{2}{3}\).

Therefore, \(y = \left(\frac{1}{2}\right)^2 = \frac{1}{4}\) or \(y = \left(\frac{2}{3}\right)^2 = \frac{4}{9}\).

(b) Use \(\tan x\) in place of \(y\) from part (a).

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

For \(\tan x = \frac{1}{4}\), \(x = 14.0^\circ\) and \(x = 194.0^\circ\).

For \(\tan x = \frac{4}{9}\), \(x = 24.0^\circ\) and \(x = 204.0^\circ\).