To calculate the roots or the solution of the equation,
we can use the quadratic formula:
x = [- b ± sqrt (b^2 – 4 a c)] / 2 a
where the coefficients are:
a = 2
b = 3
c = 6
Therefore substituting this into the equation:
x = [- 3 ± sqrt (3^2 – 4 * 2 * 6)] / 2 (2)
x = -0.75 ± [sqrt (9 – 48)] / 4
x = -0.75 ± [sqrt (-39)] / 4
x = -0.75 ± 0.25 i * sqrt (39)
x = -0.75 ± 0.25 i * (6.24)
x = -0.75 ± 1.56 i
Therefore the complex solutions are:
x = -0.75 ± 0.25 i * sqrt (39)
or
x = -0.75 ± 1.56 i
