Need some help here.

Okay, math nerds.

I'm trying to solve this math problem. I'm trying to tutor someone, and this problem is really stumping me. Any help?

3x^2 – 2x + 7 = 0, then (x-1/3)^2 = ?

I need the answer in a fraction, and how you arrived at that answer.

Alright. Let's use [2 + sqrt(-80)]/6 first. That's

[2 + 4sqrt(-5)]/6

Or

2/6 + 4sqrt(-5)/6

Or

1/3 + 2sqrt(-5)/3

Plugged into the second equation, that's

[1/3 + 2sqrt(-5)/3 - 1/3]^2

Which is

[2sqrt(-5)/3]^2

Which is (4*-5)/9, or -20/9, which is one of the answers on the sheet. Holy crap, that took forever. Thanks.