How do I know if the function is a linear function?

This is not a linear function.

Step-by-step explanation:

It is a quadratic function.  If you were to make a table of the x and y values of the function it would look like this:

x    y

0   -4

1   -1

2    8

Just by looking at these three values, we can see that they do not increase at a consistent rate.  It increases by 3 from 0 to 1, but increase by 9 from 1 to 2.  You can tell if a function is linear by seeing if it increases at a constant rate.  (In this case it does not)

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225