The method is than involving the formula (1/2)(-k+srt(k^2 +4h^3)) and the book is Liebeck's "A Concise Introduction to Pure Mathematics". Hopefully that is familiar to someone.
x^3 - 6x + 13x - 12 = 0
Let y = x-2
So y^3 = x^3 - 6x + 12x - 8
So y^3 + x - 4 = 0
So y^3 + y - 2 = 0
h = 1/3 , k = -2
Pluging into the formula gives y = crt((9+2srt(2))/9) + crt((9-2srt(2))/9)
From here I am totally stuck? Is this even right so far?