# How to solve $ax^x+bx+c=0$?

How can I solve $$ax^x+bx+c=0$$ or $$ax^{x^x}+bx^x+cx+d=0$$ where $x^x$ and $x^{x^x}$ - tetration? Is there analogue of discriminant for it?

• I'd be absolutely flabbergasted if normal polynomial methods applied here. (And not to be discouraging, but this equation looks pretty nasty in general.) – Chris Jan 16 '18 at 5:18
• Only numerical methods will do the job. – Claude Leibovici Jan 16 '18 at 7:56