Dear Macrakis: I was the one who gave that exact solution in the first place. The golden ratio naturally appears in the 5th roots of unity; if you plot the roots in the complex plane, they form the vertices of a pentagon. This then explains why you can express a lot of trigonometric angles pi*n/5 in terms of the golden ratio. For example, cos 18 = (b/4)sqrt[2] = 5^(1/4)/2 sqrt[φ].  When you solve a quintic equation, naturally the fifth roots of unity are involved, hence why the radical solution of the quintic x^5-5x+12 = 0 can be expressed in terms of the golden ratio.  I hope it is clearer now.