SOLUTION: solve. ( 5 / x ) = ( x - 3 / 2 )

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Question 42343: solve.
( 5 / x ) = ( x - 3 / 2 )
Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
%28+5+%2F+x+%29+=+%28+x+-+%283%2F2%29+%29
x%28+5+%2F+x+%29+=+x%28+x+-+%283%2F2%29+%29
5+=+x%5E2+-+%283x%2F2%29+%29
2%2A5+=+2x%5E2+-+2%283x%2F2%29+%29
0+=+2x%5E2+-+3x+-+10
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-3x%2B-10+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-3%29%5E2-4%2A2%2A-10=89.

Discriminant d=89 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--3%2B-sqrt%28+89+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-3%29%2Bsqrt%28+89+%29%29%2F2%5C2+=+3.10849528301415
x%5B2%5D+=+%28-%28-3%29-sqrt%28+89+%29%29%2F2%5C2+=+-1.60849528301415

Quadratic expression 2x%5E2%2B-3x%2B-10 can be factored:
2x%5E2%2B-3x%2B-10+=+2%28x-3.10849528301415%29%2A%28x--1.60849528301415%29
Again, the answer is: 3.10849528301415, -1.60849528301415. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-3%2Ax%2B-10+%29