Answer
Please see the work below.
Work Step by Step
According to law of conservation of energy
$(\frac{1}{2})kx^2=mgh+mgx$
This can be rearranged as:
$x^2-(\frac{2mg}{k})x-(\frac{2mgh}{k})=0$
This simplifies to:
$x=\frac{(\frac{2mgh}{k})+\sqrt{(\frac{2mg}{k})^2+(4)(\frac{2mgh}{k})}}{2}$
$\implies x=(\frac{mg}{k})(1+\sqrt{1+\frac{2kh}{mg}})$
