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## Homework Statement

Good day,

I've been have having difficulties finding the roots of this:

Find the roots of 3ix^2 + 6x - i = 0

where i = complex number

i = sqrt(-1)

## Homework Equations

quadratic formula (apologies for the large image)

## The Attempt at a Solution

using the quadratic formula

[-6 (+-) sqrt (36 - 4(3i)i)] / 6i

= (-6/6i) + (sqrt(24)/6i)

multiplying by conjugate I get:

=i (+-) ((-6i * sqrt(24))/ 36)

I'm stuck here.

apparently the roots should have both real and imaginary parts, but I have 2 imaginary parts. ie x = Re + i Im

what exactly do I have to do next?

Thank you.