The gradient of a curve at the point \((x, y)\) is given by \(\frac{dy}{dx} = 2(x + 3)^{\frac{1}{2}} - x\). The curve has a stationary point at \((a, 14)\), where \(a\) is a positive constant.

(a) Find the value of \(a\).

(b) Determine the nature of the stationary point.

(c) Find the equation of the curve.