SOLUTION: how do i solve: 4xcubed-15xsquared-6x divided by 3x

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Question 303907: how do i solve: 4xcubed-15xsquared-6x divided by 3x
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
%284x%5E3-15x%5E2-6x%29%2F3x
3x%28%284%2F3%29x%5E2-5x-2%29%2F3x
cross%283x%29%28%284%2F3%29x%5E2-5x-2%29%2Fcross%283x%29
%28%284%2F3%29x%5E2-5x-2%29
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1.333333x%5E2%2B-5x%2B-2+=+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=%28-5%29%5E2-4%2A1.333333%2A-2=35.666664.

Discriminant d=35.666664 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+35.666664+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+35.666664+%29%29%2F2%5C1.333333+=+4.11456005331429
x%5B2%5D+=+%28-%28-5%29-sqrt%28+35.666664+%29%29%2F2%5C1.333333+=+-0.364559115814056

Quadratic expression 1.333333x%5E2%2B-5x%2B-2 can be factored:
1.333333x%5E2%2B-5x%2B-2+=+1.333333%28x-4.11456005331429%29%2A%28x--0.364559115814056%29
Again, the answer is: 4.11456005331429, -0.364559115814056. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1.333333%2Ax%5E2%2B-5%2Ax%2B-2+%29