How do i solve: 1/2(r+2)^2 = 1/3(2r-1)^2? The answer is supposed to be (-7+/-3√5)/2... how?

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How do i solve: 1/2(r+2)^2 = 1/3(2r-1)^2? The answer is supposed to be (-7+/-3√5)/2... how?

Mathematics
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5r^2-14r-10=0 solve this one
it's 1.02255386... if I use the quadratic formula.
1,4+/-0,6*(11^0.5)

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what? I'm so confused..
\[\frac12(r+2)^2=\frac13(2r-1)^2\]\[3(r+2)^2=2(2r-1)^2\]\[3(r^2+4r+4)=2(4r^2-4r+1)\]\[3r^2+12r+12=8r^2-8r+2\]\[5r^2-20r-10=0\]\[r^2-4r-2=0\]\[r=\frac{4\pm\sqrt{4^2-4(-2)}}{2}=2\pm\sqrt6\]...do I have the original problem right?
yes you did. Why is it 3(r+2)^2 = 2(2r-1)^2?
for the second step?
multiply both sides by 6
why by 6?
to get rid of the fractions and make life easier
(because 6 is the LCM of 2 and 3 if you want to think about it technically...)
ohh, okay. I get it now, thank you!
welcome, but it's not the answer you wanted...

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