columbslaw — 2 discussions

$$ r_{\max}=\sqrt{\frac{kq^2}{4mg}} $$ $$ r_{\min}=\sqrt{\frac{k|q|}{E_{\mathrm{crit}}}} $$

I have tried to solve this problem by using the Columb's Law. Basically, I draw the graph and attempted to find the point where sum of the forces are zero. Here is what I have. Is there anything wrong in my working? Why can't I solve d in terms of a?