SOLUTION: (8/x) - 8 = x/(2x-1)

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Question 1086244: (8/x) - 8 = x/(2x-1)
Found 2 solutions by Fombitz, rothauserc:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%288%2Fx%29+-+8+=+x%2F%282x-1%29
8+-+8x+=+x%5E2%2F%282x-1%29
8%282x-1%29+-+8x%282x-1%29+=+x%5E2
%2816x-8%29+-+%2816x%5E2-8x%29+=+x%5E2
-16x%5E2%2B24x-8=x%5E2
-17x%5E2%2B24x-8=0
17x%5E2-24x%2B8=0
Complete the square,
17%28x%5E2-%2824%2F17%29x%29%2B8=0
17%28x%5E2-%2824%2F17%29x%2B%2812%2F17%29%5E2%29%2B8=17%2812%2F17%29%5E2
17%28x-12%2F17%29%5E2=144%2F17-136%2F17
17%28x-12%2F17%29%5E2=8%2F17
%28x-12%2F17%29%5E2=8%2F17%5E2
x-12%2F17=0+%2B-+sqrt%288%29%2F17
x=12%2F17+%2B-+%282sqrt%282%29%29%2F17
highlight%28x=%2812+%2B-+2sqrt%282%29%29%2F17%29

Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(8/x) - 8 = x/(2x-1)
:
multiply both sides of = by (2x-1)
:
(8/x)(2x-1) - 8(2x-1) = x
:
16 -8/x - 16x +8 = x
:
multiply both sides of = by x
:
16x -8 -16x^2 +8x = x^2
:
17x^2 -24x +8 = 0
:
use quadratic equation to solve
:
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x = (24 + square root(24^2 -4(17)(8))) / 2(17) = 0.8723
x = (24 - square root(24^2 -4(17)(8))) / 2(17) = 0.5395
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