SOLUTION: The reciprocal of two times a certain integer plus the reciprocal of two more times than twice the integer equals 7/24. What is the integer? Thank You

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Question 40896: The reciprocal of two times a certain integer plus the reciprocal of two more times than twice the integer equals 7/24. What is the integer?
Thank You
Found 2 solutions by Nate, Paul:
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2F%282x%29%29+%2B+1%2F%282x+%2B+2%29+=+7%2F24
%281%2F%28%282%29%28x%29%29%29+%2B+1%2F%282%28x+%2B+1%29%29+=+7%2F24

%28x+%2B+1%29+%2B+%28x%29+=+%2814x%5E2+%2B+14x%29%2F24
24%28x+%2B+1%29+%2B+24%28x%29+=+24%2814x%5E2+%2B+14x%29%2F24
24x+%2B+24+%2B+24x+=+14x%5E2+%2B+14x
0+=+14x%5E2+-+34x+-+24
0+=+7x%5E2+-+17x+-+12
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%2817+%2B-+sqrt%28+289%2B336+%29%29%2F%2814%29+
x+=+%2817+%2B-+25%29%2F%2814%29+
x+=+%2817+%2B-+25%29%2F%2814%29+
x+=+3 or x+=+-4%2F7
Your answer is: 3

Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
EQUATION:
1%2F2x%2B1%2F%282%2B2x%29=7%2F24
%28%282%2B2x%29%2B%282x%29%29=%287%282x%2B2%29%282x%29%29%2F24
2%2B4x=%2828x%2B28x%5E2%29%2F24
48%2B96x=28x%2B28x%5E2
28x%5E2-68x-48=0
Can you solve that ?
you should get x=3
Hence, the number is 3.
Paul.