SOLUTION: This operation is tough for me, I think I may know but it would help out greatly if I was shown how it works. Thank you {{{3((1/(5x)) -(2/(5x))) + 6 = (1/6)(3x-2)}}} Also if

Algebra ->  Signed-numbers -> SOLUTION: This operation is tough for me, I think I may know but it would help out greatly if I was shown how it works. Thank you {{{3((1/(5x)) -(2/(5x))) + 6 = (1/6)(3x-2)}}} Also if       Log On


   

Question 541888: This operation is tough for me, I think I may know but it would help out greatly if I was shown how it works. Thank you
3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29
Also if you could show how it is checked
Thanks again.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29
3%28-%281%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29
-3%2F%285x%29+%2B+6+=+%281%2F6%29%283x-2%29 multiply everything by the common denom (5x*6)
%285x%2A6%29%2A%28-3%2F%285x%29%29+%2B+%285x%2A6%29%2A6+=+%281%2F6%29%285x%2A6%29%283x-2%29 do cancelations

-18+%2B+180x+=+15x%5E2-10x%29
-18+%2B+180x+=+15x%5E2-10x%29 subtract 180x
-18+=+15x%5E2-190x%29add 18
0+=+15x%5E2-190x%2B18%29
quadratic formula
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 15x%5E2%2B-190x%2B18+=+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=%28-190%29%5E2-4%2A15%2A18=35020.

Discriminant d=35020 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--190%2B-sqrt%28+35020+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-190%29%2Bsqrt%28+35020+%29%29%2F2%5C15+=+12.5712104651075
x%5B2%5D+=+%28-%28-190%29-sqrt%28+35020+%29%29%2F2%5C15+=+0.0954562015591658

Quadratic expression 15x%5E2%2B-190x%2B18 can be factored:
15x%5E2%2B-190x%2B18+=+15%28x-12.5712104651075%29%2A%28x-0.0954562015591658%29
Again, the answer is: 12.5712104651075, 0.0954562015591658. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+15%2Ax%5E2%2B-190%2Ax%2B18+%29

x=12.5712 , 0.0954
3%28%281%2F%285x%29%29+-%282%2F%285x%29%29%29+%2B+6+=+%281%2F6%29%283x-2%29

3%28%281%2F.477%29-%282%2F.477%29%29+%2B+6+=+%281%2F6%29%28.2862-2%29
3%28-1%2F.477%29+%2B+6+=+%281%2F6%29%28-1.7138%29
%28-3%2F.477%29+%2B+6+=+%28-.2856%29
-6.28+%2B+6+=+-.28
-.28=-.28
correct
you would do same with other x value to check