Can someone explain to me what the hell I'm doing wrong here?
This isn't Homework I'm required to turn in, it's simply for me to practice, but I'm having a difficult time understanding why I'm failing to come to the correct answer.
I have the answer key which is the only reason I know I'm doing it wrong.

The problem, "The effectiveness of a television commercial depends on how many times a viewer watches it. After some experiments an advertising agency found that if the effectiveness E is measured on a scale of 0-10, then E(n) = 2/3n - 1/90n^2
Where n the is the number of times a viewer watches a given commercial. For a commercial to have maximum effectiveness, how many times should a viewer watch it?"

So, I attempt to convert their version of the equation into a standard form first.
-1/90x^2 + 2/3x
Factor the leading coefficients out.
-1/90 (x^2 - 60x)
Then change the interior number to allow for further factoring by halfling the b coefficient and squaring it. (60/2 = 30, 30^2 = 900)
-1/90 (x^2 - 60x + 900)
However, to balance the equation, I need to do the opposite operation on the outside of the parenthesis, and remember to multiply by the parenthesis coefficient. (900 x -1/90 = -10 is the equivalent for the inside, so I need to add ten to the outside of the equation).
-1/90 (x^2-60x+900) + 10

I would think, that the outside number, 10, is equivalent to the corresponding y coordinate of the vortex for this graph, and thus the "maximum" and answer to the original question of how many times one should view an advertisement for maximum effectiveness.
BUT
the answer key in the book says it's actually 30.

Where the hell am I going wrong.
I want to shove my head into the wall.