Thank you i advance :-)
Hey mrtn.
Hint: Take the -dS/Q^2 term to the RHS side and then take the reciprocal of both sides which will give Q^2/dS = blah. After this you multiply both sides by dS and take the square root.
Show us your attempts so we can guide you through them.
Question: What is the subscript on h for?
I would move the fraction with Q^2 to the right hand side of the equation to start.
$\displaystyle \frac{h}{2} - \frac{dh}{2p} = \frac{ dS}{Q^2} $
Combine fractions on the left
$\displaystyle \frac{h(p - d)}{2p} = \frac{dS}{Q^2} $
Divide both terms in the parenthesis by p
$\displaystyle \frac{h(1 - \frac{d}{p})}{2} = \frac{Q^2}{dS} $
Invert both sides
$\displaystyle \frac{2}{h(1 - \frac{d}{p})} = \frac{Q^2}{dS} $
Multiply by dS
$\displaystyle \frac{2Sd}{h(1 - \frac{d}{p})} = Q^2 $
Extract the root
$\displaystyle Q = \pm \sqrt{\frac{2Sd}{h(1 - \frac{d}{p})}} $
Question: What is the subscript on h for?