The answer to the question, as stated, is that it is a quadratic equation in one unknown, x.
The solution to the equation is as follows:
x2 - 6x - 7 = 0 ie x2 - 7x + x - 7 = 0 or x(x-7) +1(x-7) = 0
(x+1)(x-7) = 0 so that x+1 = 0 or x-7 = 0 and so x = -1 or x = 7.
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x2 + 6x = 7 ⇒ x2 + 6x + 9 = 7 + 9 ⇒ (x + 3)2 = 16 ⇒ x + 3 = ±4 ⇒ x = -7 or 1
y = x2 - 6x + 2 y = x2 - 6x + 9 - 7 y = (x - 3)2 - 7
7 - 6x- x2 = 0 so changing signs and reordering, x2 + 6x - 7 = 0 then x2 + 7x - x - 7 = 0 that is x(x + 7) - 1(x + 7) = 0 so that (x - 1)*(x + 7) = 0 which implies that x - 1 = 0 ie x = 1 or x + 7 = 0 ie x = -7
x^2 + 3x + 7 = 6x + 18 x^2 - 3x - 11 = 0
x2 - 14x = -49 ∴ x2 - 14x + 49 = 0 ∴ (x - 7)2 = 0 ∴ x = 7