x = (32 +/- sqrt(256)) / 6
x = (32 +/- 16) / 6
x = 48/6 , 16/6
x = 8 , 4/3
Now, x = 8 can't be a correct answer, since the overall length of x and 4 - x is 4 units
x = 4/3
There's the hard part; finding x. Now, all we have to do is find the angles:
tan(t[1]) = 2/(4/3)
tan(t[2]) = 1/(4 - (4/3))
Does tan(t[1]) = tan(t[2])?
tan(t[1]) = 6/4 = 3/2
tan(t[2]) = 1 / (12/3 - 4/3) = 1 / (8/3) = 3/8
Obviously, there's a problem. I can't see where I messed up, but I did notice that if I switched some values, the tangents are equal:
tan(t[1]) = 2 / (4 - x) = 2 / (4 - 4/3) = 2 / (8/3) = 2 * (3/8) = 3/4
tan(t[1]) = 1 / (4/3) = 1 * (3/4) = 3/4