The shaded region is bounded by \(y=\sqrt{6x+5}\), the \(x\)-axis, and \(x=a,x=2a\), where \(a>0\). Rotation through \(360^\circ\) about the \(x\)-axis gives volume \(V\ge46\pi\).

(a) Show \(9a^2+5a-46\ge0\). [4]

(b) Find the range of possible \(a\). [3]