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is this correct:

solve:

5(x-2)^2=3

My answer:

(10 +/- sqrt 15)/(5)

looks like you expanded, then used the formula and you got the right answer properly reduced.
I think you are getting this!!!

I don't want to confuse you but I would have done the following:

(x-2)^2 = 3/5
x-2 = +/- sqrt(3)/sqrt(5)
x = 2 +/- sqrt(3/5)

test it with a calculator, you'll get the same decimal answer.

so my answer should like your or mine?

Both your answer and the alternate answer are correct. Your answer, (10 +/- sqrt 15)/(5), is the result of expanding the equation, applying the quadratic formula, and properly reducing the expression. The alternate answer, x = 2 +/- sqrt(3/5), is the result of isolating x and taking the square root of both sides directly. Both answers are equivalent and will give you the same decimal value when calculated. So, you can confidently choose either answer!