How to solve equations using continued fractions?

[Arian.D]

Is it possible to solve any equation if we use continued fractions? I've heard that polynomial equations could be solved using continued fractions, and I used to obtain one of the several roots of a polynomial equation of low degrees using continued fractions in high school, but I read somewhere that continued fractions could be employed to find rapid converging sequences to the roots of an equation and I guess I even read somewhere that they could be used to solve differential equations!

Could someone inform me about the use of continued fractions to solve equations please? Thanks in advance.

 

[fresh_42]

I've found some applications of continued fractions ( http://www.rnta.eu/SecondRNTA/Waldschmidt-Sanna.pdf ) and in section 5 exponential Diophantine equations. Also Pell's theorem plays a role, but I haven't seen applications on general roots. I guess there are better algorithms, and from degree 5 onwards we only have numerical methods.