Complete the square:
x² - 4x + 6 = 0
x² - 4x = -6
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
But the left side is positive for any real number x, so there are no real solutions.
If you're solving over the complex numbers, we can go on to say
x - 2 = ± √(-2)
x - 2 = ± 2i
x = 2 ± 2i
where i = √(-1).
