Does solving mathematical equations with Cellular Automata structures means it is universal?
If you can solve arbitrary equations involving an arbitrary number of unknowns, then you have shown universality, as explained below.  So there is a sense in which your broad question "solving mathematical equations means universality" is actually true -- but we have to precisely define what "mathematical equations" mean here. From your actual examples it seems you are not at the final goal of showing universality: it is not sufficient to solve ploynomial equations in a single variable.

If the equations you can solve are so-called Diophantine equations, then your system is universal.  That is, polynomials with multiple variables and integer coefficients, and solved with solutions in the natural numbers. According to the solution of Hilbert's tenth problem such equations encode recursively enumerable sets (of natural numbers). The question whether the polynomial can have value $0$ with fixed `input' value of the first variable codes membership of that value in the set we compute. Or as wikipedia states: "Every recursively enumerable set is Diophantine". This seems universal to me. 

To see how complicated these polynomials can be, have a look at this Formula based on a system of Diophantine equations for the prime numbers. (This example generates prime numbers, so is slightly different, but can be tweaked.)

The right definition of universality is not always clear. We must encode input and output in a way suitable to the machine at hand (here the cellular automaton) without giving away parts of the solution. I remember some controversy concerning this.