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"I got on a test question that:

3x^2 - 2x + 7 = 0, then ( x - 1/3 )^2 = ???

The correct is -20/9. I don't see how this is possible since you get a negative number under the radical sign (-80) when using the quadratic formula.

Could you explain this? Thanks...."

What you are discovering are imaginary numbers. These are legitimate numbers that crop up in many situations. They can be written as a real number times the square root of negative 1, which is designated

i = √-1

where the "i" stands for imaginary.

For your problem, the number under the square root sign in the quadratic equation can be written as √-80 = √(-1)(80) = i√80. The rest of the quadratic solution is

x = 1/3 ± i(√80)/6.

Subtracting 1/3 and taking the 6 into the square root gives

(x-1/3)^2 = [ i(80/36)^1/2 ]^2 = i^2(80/36) = (-1)(20/9).

Imaginary numbers are a little strange but they do exist and are important in mathematics. Don't worry if you have trouble understanding them, it took mathematicians a long time to accept them, too.

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