I have a problem that I can't seem to solve neither analytically nor with Mathematica. Namely, I have the expression $$x^{b^2} + ax^b - 1= 0,$$ which I want to solve for $x$ with $a>0$, $b>1$. 

But I can't find a method in Mathematica that would provide an answer to this without specifying $a$ and $b$ (for example, Solve, Root, FindRoot and Reduce don't work). I am quite new to the software, however, so I was wondering whether I am just missing something or can this equation truly not be solved in general using it?