Question

4x2 + x = -3 how do people get an "i" term ?

Answer 1

4x² + x = -3

You need to use the quadratic formula to solve this. First make sure to get everything on one side so the equation equals 0.
4x² + x + 3 = 0

x = (-b +/-√b² - 4ac)/2a
x = (-1 +/-√1² - 4(4)(3))/2(4)
x = (-1 +/-√1 - 48)/8
x = (-1 +/-√-47)/8

Now before you continue, remember that you can't have a negative number in the square root. √-47 is the same as √47 × √-1. 
√-1 is the same thing as i, so you can take that out.
It will now look like this: i√47
So now you can continue doing the problem.

x = (-1 +/- i√47)/8
x = -1/8 +/- (i√47)/8
This can't really be simplified further.

So if you are meant to put it in a + bi form, then the answers would be:
x = -1/8 + (i√47)/8
x = -1/8 - (i√47)/8