(a) Write \(19-12x-3x^2\) in the form \(a(x+b)^2+c\), where \(a\), \(b\) and \(c\) are integers.

(b) Hence find the maximum value of \(19-12x-3x^2\) and the value of \(x\) at which this maximum occurs.

(c) Use your answer to part (a) to solve the equation \(19-12\sqrt u-3u=0\).