The sum of the squares of three consecutive integers is greater than three times the square of the middle integer by 2 . Using $x$ to represent the highest of the three integers, translate this information in terms of $x$ to form an equation.

Step 1 ：Let the three consecutive integers be \(x-1\), \(x\), and \(x+1\), where \(x\) is the highest integer.

Step 2 ：The sum of the squares of these integers is: \((x-1)^2 + x^2 + (x+1)^2\)

Step 3 ：Three times the square of the middle integer is: \(3 * x^2\)

Step 4 ：According to the given information, the sum of the squares is greater than three times the square of the middle integer by 2. So, we can write the equation as: \((x-1)^2 + x^2 + (x+1)^2 = 3 * x^2 + 2\)

Step 5 ：\(\boxed{(x-1)^2 + x^2 + (x+1)^2 = 3 * x^2 + 2}\) is the equation representing the given information.