Given below are 3 equations I, II and III where 'a' and 'b' are the roots of equation I where (a < b) and 'c' and’d’ are roots of equation II where (c < d). On this basis, solve for equation III and find the relationship between 'z' and 'k' given that k = 11
I. 3x(x - 12) + 72 = x2 - 11x - 5
II. 5y(y - 3) - 64 = y(3y - 2) – 19
III. (z + 2a - d)2 = 169