exam Maths Puzzle Numerical Ability

I need help with 3x^2 - 2x + 1 = 0

I came out with x = 2/6 + sqrt 8/6

Did I do this right?

I see the answer, but am confused on what the "i" means?

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How do you find a fraction between a pair of fractions. ex: 7/12, 3/4
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I have to do a really big project and I got stuck doing this. I do not know what is means. What is an algebraic expression using equations and inequalities? Will you give me examples of each.