Find Centroid of Bounded Region: Accurate to 0.001

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Find the centroid of the region bounded by y = 1.5x2 − 14x + 23.5, and xy = 8. You should enter the coordinates of your answer either as decimals or fractions. Your answer must be accurate to within 0.001.

I got a wrong answer of (7/3, 59/52), I'm having problems plugging in the numbers. Any help would be appreciated.

Mod note: Warning issued because now work was shown and the template was not used.
 
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You should use the HW template and post questions like these in the appropriate HW forum.

If you still want help, please show your work.
 
Start by plotting the curves. The picture would show you that your first answer was not even in the region enclosed.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...

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