You can put this solution on YOUR website!
Use the information you are given to build things up.
Let the unknown number be X.
Its square is: X²
one half of its square is: X²/2
twice the number is: 2X
twice the number plus 6 is: 2X + 6
Equate the two phrases, which you are told are equal,
X²/2 = 2X + 6
multiplying up and moving all terms to the one side, we get a quadratic,
X² - 4X - 12 = 0
which factorises as,
(X-6)(X+2) = 0
therefore: X = 6, X = -2
If we can ignore negative values then there is only one solution,
X = 6