Missing factor of 2 in an equilibrium problem

[Eggue]

Homework Statement

A heavy horizontal girder of length L has several objects suspended from it. It is supported by a frictionless pivot at its left end and a cable of negligible weight that is attached to an I-beam at a point a distance h directly above the girder’s center. Where should the other end of the cable be attached to the girder so that the cable’s tension is a minimum?

Relevant Equations

Conditions for equilibrium

I honestly have no idea where I'm going wrong
i've checked my differentiation using a derivative calculator but the answer is the same.
The answer from the book is $\frac{L}{2} + \frac{h^2}{L}$

Working:

 

[Cutter Ketch]

I have worked it independently and get your answer.