Question 4269
Assign the variables:  Let x = the length of the side of the square.
Then x+6 = the length of the diagonal. 

Apply the Pythagorean theorem:  c^2 = a^2 + b^2   c is the diagonal, a and b are the sides of the square.

(x+6)^2 = x^2 + x^2
x^2 + 12x + 36 = 2x^2     Subtract x^2 from both sides.
12x + 36 = x^2         Rewrite in standard quadratic form.

x^2 - 12x - 36 = 0      Solve the quadratic using the quadratic formula.

{{{x=(-b+-sqrt(b^2-4ac))/2a)}}}
{{{x=(12+-sqrt(-12^2-4*36))/2)}}}