I hate fractions, but I don't usually get them wrong. I didn't really get this one wrong, but I'm not really sure of the complete process with this one.

I'm 22 and since I dropped out of high school, I plan on getting my GED, so I bought a college algebra book. The book is "McGraw Hill - College Algebra Demystified" and it seems like a pretty good book, but lacks a lot explanations. I have done quadratic equations before, but not radicals with fractions.

This is the problem: 3x^2+9x-2=0

I'm on the first chapter of this book and I'm completing the square and I don't have any problem there. The problem is with my answer and their extra step with the fraction.

I end up with: x = -3/2 + √35/12 and -3/2 - √35/12

The books answer is: x = -3/2 + √105/6 and -3/2 - √105/6

I understand that you get: 2√3 for 12. But why are the numerator and denominator both multiplied by 3?

I feel crazy asking this question, because I can see how it's done, but I need an explanation on the last part.