You can solve this by "completing the square." I find it easier to put the constant by itself on one side of the equal sign for that.
x^2 - 4x - 7 = 0
x^2 - 4x = 7 (add 7 to both sides)
x^2 - 4x + 4 = 7 + 4 (complete the square by adding (4/2)^2)
(x - 2)^2 = 11 (simplify)
x - 2 = ±√11 (square root both sides)
x = 2 ± √11 (add 2 to both sides)
x^2 - 4x - 7 = 0
x^2 - 4x = 7 (add 7 to both sides)
x^2 - 4x + 4 = 7 + 4 (complete the square by adding (4/2)^2)
(x - 2)^2 = 11 (simplify)
x - 2 = ±√11 (square root both sides)
x = 2 ± √11 (add 2 to both sides)