calculate roots with negative power and two variables

Question

i want to calculate roots for following equation. which has $2$ variables $x$ and $h$, where $h$ has some negative power. $h^2*A+144*h^{-1/2}*B=0$ where $A$ and $B$ both are some function of $x$. I want roots of $h$ only. please help me in this manner.

Answer 1

$h^2 .A=-144 . B h^{-1/2}$

$A^2 .h^4= 144^2. B^2. h^{-1}$

$A^2. h^5=144^2.B^2$

$h=(\frac{144^2.B^2}{A^2})^{1/5}$