  In this work, the Lambert-Tsallis Wq function is used to provide analytical
solutions of fractional polynomials of the type ax^r+bx^s+c = 0. This class of
fractional polynomial appears in several areas of physics as well it is in the
heart of some famous mathematical problems, like the Fermat and Fibonacci
equations. Therefore, analytical solutions for the equations A^x + B^x = C^x
and q1^x-q2^x=ysqrt(5), where q1=(1+sqrt(5))/2 and q2=(sqrt(5)-1))/2, are also
provided.
