SOLUTION: 20/x+1 -( x/2) +1 is less than or equal to 0 Can someone help me with this one, please? Once I go into factoring, i lose myself. Solve the nonlinear inequality. Express th

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Question 992340: 20/x+1 -( x/2) +1 is less than or equal to 0

Can someone help me with this one, please? Once I go into factoring, i lose myself.
Solve the nonlinear inequality. Express the solution using interval notation.
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!

20/(x+1) -( x/2) +1 <= 0
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Assuming x > -1 (to keep x+1 > 0), you get:
40 - x(x+1) < 0
40 - x^2 - x < 0
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x^2 + x - 40 > 0
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Solve the EQUALITY::
x = [-1+-sqrt(1-4*-40)]/2
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x = [-1 +- sqrt(161)]/2
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These are the zero values of the quadratic.
The values greater than zero are to the left of [-1-sqrt(161)]/2
and to the right of [-1+sqrt(161)]/2
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ans: Since x > -1, the solution is x > [-1+sqrt(161)]/2
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Cheers,
Stan H.