x 2 = -1

for what does the kind of mix between '+' and '=' stands for?

The +- symbol means that the number can be both positive and negative. So, to elaborate on Meoldy's answer, x = -i and  x = +i. You use it whenever you take the square root of a number, as both (-x)^2 and (x)^2 give the same result, without exception.
You'll see this in the quadratic formula: $x = {-b \pm \sqrt{b^2-4ac} \over 2a}$

That just means there are two answers, one where the +- sign is positive and one where it's negative.

Thanks ThisGuy.  :)

It really means  x=i    OR    x = -i

x obviously cannot equal both at once and that is what 'and' means :)

It is a technical difference but it is an important one for both of you to understand :)