4x^2-4 radical3x +3=0 Using quadratic formula

4x^2 - 4√3 x + 3 = 0

a = 4
b = -4√3
c = 3

x = (4√3 ± √(48 - 4(4)(3)) )/8
= (4√3 ± √0)/8
= 4√3/8
= √3/2 mmmh, only one root, but quadratics have two roots, so √3/2 must be a double root and the expression must be a perfect square

check: factors should be
(2x + √3)(2x + √3)
= 4x^2 + 2√3 x + 2√3 x + 3
= 4x^2 + 4√3 x + 3

so x = √3/2 is the solution.