Close, except that -8 + 4 = -4, divided by 8 is -.5, and -8 - 4 = -12, divided by 8 = -1.5.
Other then that, it was right.
And I learned it this way:
4X² + 8X + 3 = 0 is:
(2X+1)(2X+3) = 0
(2X+1) = 0
X = -.5
(2X+3) = 0
X = -1.5
Then it's just a matter of checking the above equation with the two values of X.
This method is just FOIL factoring the equation, which takes some trial and error, I like the method you used, I can't quite describe it, I tried to, but I ended up not making any sense. =P