Singular

Hello to everybody.
I am the beginner here and I need your help.

I want to find the roots of polynom (its degree is 2) using puiseux series in tropical mathematics (or may be using other method)
(tropical sum is the maximum, tropical multiplication is ordinary addition)

For example f=(1+t)+t^2x+tx^2
x1=it^(-1/2)+1/2it^(1/2)-1/2t+...
x2=-it^(-1/2)+...

Also in future I want to find the solution of non-linear system 2х2
in tropical sense.

I found singular and have allready appreciated its advantages.
Thanks to its developpers!
May be this task is solved or there is something close to its solution.

With respect to you and with the expectation of reply.
Fedor.