In a square with side length of 6, what is the distance between the center of the square and the center of the largest equilateral triangle inscribed inside the square?

Place the right angle at the origin. Short leg on x-axis.
The forth corner of the square is the point on the hypotenuse where the line y = x intersects. (Draw a diagram!)
In this case the hypotenuse is y = -4x/3 + 8
x = -4x/3 + 8
7x/3 = 8
7x = 24
x = 3.428571429

The solution to the system of equations (-2,2)