There can be a couple of ways to do this. Myself, I like to add 7 to both sides first. That gives us:
4x^2 + 12x = 7
Then, I divide each side by 4. That gives us:
x^2 + 3x = 7/4
Because, dividing the left side by 4, you have to divide 4x^2 and 12x by 4, both of them.
Then, you take half of 3 and square that result. Half of 3 is 1.5. Squaring that, we have 2.25. We add that to each side. Thus:
x^2 + 3x + 2.25 = 4
That 2.25 allows the left side to be factored into (x+1.5)^2
(x+1.5)^2 = 4
Taking the square root of each side:
x+1.5 = +-2
subtracting 1.5 from each side:
x = -1.5 +- 2 = -3.5, 0.5
So, x = -3.5 and x = 0.5
Good Luck, Rosey. I hope you understand the method.