SOLUTION: 2/3x-7=x

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: 2/3x-7=x      Log On


   



Question 154734This question is from textbook Algebra structure and method book 1
: 2/3x-7=x This question is from textbook Algebra structure and method book 1

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
2/3x-7=x
------------
Multiply by 3x
2 - 21x = 3x^2
3x^2 + 21x - 2 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B21x%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=%2821%29%5E2-4%2A3%2A-2=465.

Discriminant d=465 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+465+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2821%29%2Bsqrt%28+465+%29%29%2F2%5C3+=+0.0939764421413039
x%5B2%5D+=+%28-%2821%29-sqrt%28+465+%29%29%2F2%5C3+=+-7.0939764421413

Quadratic expression 3x%5E2%2B21x%2B-2 can be factored:
3x%5E2%2B21x%2B-2+=+%28x-0.0939764421413039%29%2A%28x--7.0939764421413%29
Again, the answer is: 0.0939764421413039, -7.0939764421413. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B21%2Ax%2B-2+%29