How to derive a Tangential Portfolio using the Quadprog function

Hello Folks.

I'm not sure i'm asking in the right place but i currently have a problem. I've heard that the Quadprog function in Matlab from the Optimization Toolbox is used to find the Portfolio with the highest sharpe ratio (Tangential Portfolio). However i think my Code works (using QP giving plausible results) but the thing is i don't have a "Derivation" on that matter why i'm using Quadprog. So my Problem is more a mathematical issue.

Stage 1

Sharpe Ratio Maximization: (r'w-rf)/sqrt(w'Cw) C= Var-Covar Matrix r= mean returns w = weights

Stage 2

min┬x〖1/2 x^T Hx+f^T x

x= weights H= Var-Covar Matrix

I'm totally lost because i don't know how to get from stage 1 to stage 2.

Any help is appreciated ;) and sorry for my english :D

Greetings

Matthew