The coefficients of this quadratic equation are a = 2, b = -3 and c = 6. Thus, the discriminant is b^2 - 4(a)(c), or (-3)^2 - 4(2)(6), or 9 - 48, or -39.
Thus, the roots are:
-(-3) ± i√39 3 ±i√39
x = ------------------- = ----------------
2(2) 4
This corresponds to the first of the four given answers.
