How to solve the equation of following form

Question

I have an equation of following form $$x^2e^{-ax}=c$$ where $a>0,c>0$. I want to know how to solve the above equation for $x$. I know how to solve the equation of the form $xe^{-ax}=g$(using Lambert function) but I am not sure about the equation written above. Any help in this regard is much appreciated. Thanks in advance.

Answer 1

$$ x\mathrm{e}^{-ax/2} = \pm\sqrt{c}\implies -\frac{xa}{2}\mathrm{e}^{-ax/2} =\mp\frac{a\sqrt{c}}{2} $$ You should be able to manipulate this.