Since we don't know the number we'll call it x. The problem says that x squared - 7 = 6 times x.
As an equation we can write this as
x2 - 7 = 6x
To solve this, we subtract 6x from both sides to set the equation equal to 0
x2-6x-7 = 0
Now we can factor or use the quadratic equation to find what x equals. In this case it's easier to factor:
(x-7)*(x+1) = 0
So the positive solution is x = 7.