Your equation has complex solutions. They can be found by "completing the square" or by using the quadratic formula.

4x^2 - 4x + 3 = 0

4x^2 - 4x = -3 (removing the constant from the left side can make it easier to see how to complete the square)

4x^2 - 4x + 1 = -2 (add (b^2)/(4a) to make ax^2 + bx into a perfect square)

(2x - 1)^2 = -2 (rewrite as a square)

2x - 1 = ±√(-2) = ±I√2 (take the square root of both sides)

2x = 1 ± I√2 (add 1)

4x^2 - 4x + 3 = 0

4x^2 - 4x = -3 (removing the constant from the left side can make it easier to see how to complete the square)

4x^2 - 4x + 1 = -2 (add (b^2)/(4a) to make ax^2 + bx into a perfect square)

(2x - 1)^2 = -2 (rewrite as a square)

2x - 1 = ±√(-2) = ±I√2 (take the square root of both sides)

2x = 1 ± I√2 (add 1)

**x = (1 ± I√2)/2**(divide by 2)