Can you please help me rearrange this equation and make z the subject:
x = z +1/4z
Both satx and Amber Lamps assumed that you mean x= z+ (1/4)z.
If you meant, instead, x= z+ 1/(4z), multiply the entire equation by 4z to get $\displaystyle 4xz= 4z^2+ 1$ which is the same as $\displaystyle 4z^2- 4xz- 1= 0$.
Solve that with the quadratic formula: $\displaystyle z= \frac{-b\pm\sqrt{b^2- 4ac}}{2a}$
with a= 4, b= -4x and c= -1.