negative 1 over 2x + 2 = - x + 7

Multiply by the denominator and solve the resulting quadratic.

... - 1 / (2x + 2) = - x + 7

... - 1 = (2x + 2) (-x + 7)

... 2x^2 - 12x - 15 = 0

And from the quadratic formula

... x = (12 ±√ ((-12) ^2 - 4 (2) (-15))) / (2 (2))

... x = 3 ±√16.5

x ≈ - 1.062019 or 7.062019