SOLUTION: Find a number such that the sum of the number plus 12 times its reciprocal is 8. There are two solutions. How do I do this problem? Could you show me the steps?

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Question 29633: Find a number such that the sum of the number plus 12 times its reciprocal is 8. There are two solutions. How do I do this problem? Could you show me the steps?
Answer by Paul(988) About Me  (Show Source):
You can put this solution on YOUR website!
Let the number be x
Equation:

x%2B12%281%2Fx%29=8 mulitply the whole equation by x to remove the fraction
x%28x%2F1%29%2Bx%2812%2Fx%29=x%288%2F1%29
x%5E2%2B12=8x
x%5E2-8x%2B12=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%28-%28-8%29%2B-sqrt%28%28-8%29%5E2-4%2A1%2A12%29%29%2F%282%2A1%29
Simply you get two solutions:

x=2 and x=6
Hence, the number is 2 or the number is 6.
Paul.