on my electronics book I found some equations in which there are $\Delta x$ and these are handled with the same rules of differential. For example, if $a$ is a constant:
$$\Delta \left(ax\right)=a\Delta x$$
What kind of quantities are $\Delta x$? Maybe finite differentials?
Thank you for your help.
To avoid confusion, let me write $f$ instead of $x$. I do this because we can think of $f$ (or $x$) as a function. I don't know the exact situation in your book, but this is not uncommon.
If $f$ is a measure of something, then $\Delta f$ usually means a difference (or increase) in $f$. So $f$ could be a height, voltage, velocity, etc.
You can, often, think of $f$ as a function of time $t$. If $t$ changes from $t_1$ to $t_2$, then we would say that $\Delta f = f(t_2) - f(t_1)$. If you do that, then $\Delta f$ is the change in $f$ over a certain time interval ($t_2 - t_1$).
Now, the question then is why $\Delta af = a\Delta f$.
If $f$ is a function that tells you the height of something as a function of time $t$, then $af$ gives you $a$ times that height $f$. You simply multiply all the values of the function by $a$. So $af$ is a new function. Then from $t_1$ to $t_2$, then change is $$\Delta af = af(t_2) - af(t_1) = a(f(t_2) - f(t_1)) = a\Delta f.$$