To solve this equation, first move all terms to one side to set the equation to zero:

x² - 2x + √11 -3 = 0

Now, this is a quadratic equation in the form of ax^2 + bx + c = 0. To solve for x, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / 2a

In this case, a = 1, b = -2, and c = √11 - 3. Plugging these values into the quadratic formula, we get:

x = (2 ± √((-2)^2 - 41(√11 - 3))) / (21)
x = (2 ± √(4 + 4√11 - 12)) / 2
x = (2 ± √(4√11 - 8)) / 2
x = 1 ± √(√11 - 2)

Therefore, the solutions to the equation x² - 2x + √11 -3 = 0 are x = 1 + √(√11 - 2) and x = 1 - √(√11 - 2).