solve quadratic equation x2 + x + (sqrt 3/4)i = 0 complex roots

Answer 1

x^2 + x + (√3/2)i = 0
2x^2 + 2x + √3 i = 0

x = (-2 ± √(4 - 8√3 i)/4
= (-2 ± 2√( 1 - 2√3 i) )/4
= ( -1 ± √(1-2√3 i)/2