The square of an integer is 812 greater than the integer itself. What is the sum of all integers for which this is true?

"The square of an integer is 812 greater than the integer itself. What is the sum of all integers for which this is true?"

Let n be the integer.

Then we have n^{2} - 812 = n or n^{2} - n - 812 = 0

This factors as (n + 28)(n - 29) = 0

You can take it from here.