SOLUTION: 4/7 (3-2x)- 8/3x + 2

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Question 146248: 4/7 (3-2x)- 8/3x + 2
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F7+%283-2x%29-+8%2F3x+%2B+2
Multiply thru by 21x to eliminate fractions.
12x%2A%283-2x%29+-+56+%2B+42x+=+0 (I assume you meant = to zero.)
(((36x - 24x^2 - 56 + 42x = 0}}}
Collect terms
-24x%5E2+%2B+78x+-56+=+0
12x%5E2+-+39x+%2B+28+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 12x%5E2%2B-39x%2B56+=+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=%28-39%29%5E2-4%2A12%2A56=-1167.

The discriminant -1167 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -1167 is + or - sqrt%28+1167%29+=+34.1613817050774.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+12%2Ax%5E2%2B-39%2Ax%2B56+%29

That graph isn't much help.