Solution to generalized-polynomial equation? Is it possible to obtain the solution to this generalized-polynomial equation?
$$b x^a - x +c =0$$
with $-1<a<1$, $b>0$, $c>0$ and $x>0$.

Hint: Define $$f(x)=bx^a-x+c$$ and use calculus.
$$f'(x)=bax^{a-1}-1$$
we have $$f(0)=c>0$$
if $a<0$ then we get $$f'(x)<0$$
If $0<a<1$ then we get  $$f'(x)=0$$ if $$x=\left(\frac{1}{ab}\right)^{1/{a-1}}$$
