(a) Find the equation of the normal to the curve

\(y=x^3-7x^2+12x-5\)

at the point \((1,1)\).

(b) Find the \(x\)-coordinates of the two points where the normal cuts the curve again. Give your answers in the form \(x=a\pm\sqrt b\), where \(a\) and \(b\) are integers.