What is the value of x in a 30-60-90 triangle with a hypotenuse of x+12 and a longer side of x?

In a 30 - 60 - 90 triangle the side opposite the hypotenuse is 1/2 the hypotenuse and which will be the shorter side. Read this over a couple of times till you realize that (x + 12)/2 is the shortest side.

[(x + 12) / 2]^2 + x^2 = (x + 12)^2 subtract [(x + 12)/2]^2 from both sides.

x^2 = (x +12)^2 - [ (x +12)/2]^2
x^2 = (x + 12)^2  [ 1 - (1/2)^2] You were given this as a question in school? It seems awfully hard.
x^2 = (x + 12)^2 [3/4] 
4x^2 = 3*(x^2 + 24x + 144)
4x^2 = 3x^2 + 72x + 432
x^2 - 72x - 432 = 0 This is a quadratic, do you know what they are?
The solution to this comes to x = 77.56

I don't think I made a mistake, but it is sure possible.Check the numbers and my method. 

Agc and bgd are vertical angles