SOLUTION: Solve (2a-1)=a+17/a+1?

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Question 397998: Solve (2a-1)=a+17/a+1?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
%282a-1%29=a%2B17%2Fa%2B1..........if you have17%2Fa on the right side

a%282a-1%29=a%2Aa%2B17%2Aa%2Fa%2B1%2Aa
2a%5E2-+a+=+a%5E2%2B17%2B+a
2a%5E2-a%5E2+-+a-+a+=+17
a%5E2+-+2a-+17+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A%2817%29+%29%29%2F%282%2A1%29+
x+=+%282+%2B-+sqrt%28+4+%2B+68+%29%29%2F%282%29+
x+=+%282+%2B-+sqrt%28+72+%29%29%2F%282%29+

x+=+%282+%2B-+%28+8.49+%29%29%2F%282%29+

x+=+%282+%2B-+%28+4.245+%29%29%29+

so, your a=x
and a1=+6.245, a2=+-2.245

but if you have %28a%2B17%29%2F%28a%2B1%29, then will be

%282a-1%29=%28a%2B17%29%2F%28a%2B1%29.........multiply by %28a%2B1%29

%28a%2B1%29%282a-1%29=+%28a%2B17%29%28a%2B1%29%2F%28a%2B1%29

%28a%2B1%29%282a-1%29=+%28a%2B17%29cross%28%28a%2B1%29%29%2Fcross%28%28a%2B1%29%29

%28a%2B1%29%282a-1%29=+%28a%2B17%29

2a%5E2-a+%2B2a-1=+a%2B17

2a%5E2+%2Ba-a-1=+17
2a%5E2+-1-17+=+0
2a%5E2+-18+=+0
2a%5E2%2F2+=18%2F2+
a%5E2++=+9

a = +- sqrt%289%29%29
a = +- %283%29