SOLUTION: 5/3x+1/3x=2x+40/3+8/3x The solution s x=?

Algebra ->  Equations -> SOLUTION: 5/3x+1/3x=2x+40/3+8/3x The solution s x=?      Log On


   

Question 464046: 5/3x+1/3x=2x+40/3+8/3x
The solution s x=?
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
5/3x+1/3x=6/3x
6/3x=2x+40/3+8/3x
6=6x2+40x+8
6x2+40x+2=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 6x%5E2%2B40x%2B2+=+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=%2840%29%5E2-4%2A6%2A2=1552.

Discriminant d=1552 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-40%2B-sqrt%28+1552+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2840%29%2Bsqrt%28+1552+%29%29%2F2%5C6+=+-0.050380732734632
x%5B2%5D+=+%28-%2840%29-sqrt%28+1552+%29%29%2F2%5C6+=+-6.61628593393203

Quadratic expression 6x%5E2%2B40x%2B2 can be factored:
6x%5E2%2B40x%2B2+=+6%28x--0.050380732734632%29%2A%28x--6.61628593393203%29
Again, the answer is: -0.050380732734632, -6.61628593393203. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+6%2Ax%5E2%2B40%2Ax%2B2+%29