SOLUTION: 6x^2-5x+1=0 answer:x=1/3 or 1/2 need a full break down of how my book got those fractions as answers

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Question 181636: 6x^2-5x+1=0
answer:x=1/3 or 1/2
need a full break down of how my book got those fractions as answers
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
6x%5E2+-+5x+%2B+1+=+0
You can work backwards to get the equation
from the roots, which are:
(1) x+=+1%2F3
(2) x+=+1%2F2
Subtract 1%2F3 from both sides of (1), and
Subtract 1%2F2 from both sides of (2)
(1) x+-+%281%2F3%29+=+0
(2) x+-+%281%2F2%29+=+0
Now multiply both sides of (1) by 3,
and multiply both sides of (2) by 2
(1) 3x+-+1+=+0
(2) 2x+-+1+=+0
The product of (1) and (2) will be 0 also
%283x+-+1%29%282x+-+1%29+=+6x%5E2+-+5x+%2B+1
6x%5E2+-+5x+%2B+1+=+0
-----------------------
Also, each of the roots will solve the equation
6%2A%281%2F3%29%5E2+-+5%2A%281%2F3%29+%2B+1+=+0
6%2A%281%2F9%29+-+5%2F3+%2B+1+=+0
6%2A%281%2F9%29+-+15%2F9+%2B+9%2F9+=+0
Multiply both sides by 9
6+-+15+%2B+9+=+0
0+=+0
And, also
6%2A%281%2F2%29%5E2+-+5%2A%281%2F2%29+%2B+1+=+0
6%2F4+-+5%2F2+%2B+1+=+0
6%2F4+-+10%2F4+%2B+4%2F4+=+0
Multiply both sides by 4
6+-+10+%2B+4+=+0
0+=+0
OK