The solution to your problem is as follows:
-5x^2 + 30x - y - 34 = 0
y = -5x^2 + 30x - 34
y = -5(x^2 - 6x) - 34
y = -5(x^2 - 6x + 9 - 9) - 34, by completing the square
y = -5(x^2 - 6x + 9) + 45 - 34
y = -5(x - 3)^2 + 11
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