SOLUTION: 5/14 - 2/x = 3x

Algebra ->  Equations -> SOLUTION: 5/14 - 2/x = 3x      Log On


   

Question 337454: 5/14 - 2/x = 3x
Found 2 solutions by Fombitz, edjones:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Multiply both sides by 14x,
5x-28=42x%5E2
42x%5E2-5x%2B28=0
Use the quadratic formula,
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x=%285+%2B-+sqrt%2825-4%2842%29%2828%29%29%29%2F%282%2842%29%29
x=%285+%2B-+sqrt%28-4679%29%29%2F%2884%29
x=%285+%2B-+sqrt%284679%29i%29%2F%2884%29 where i=sqrt%28-1%29

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
5/14 - 2/x = 3x
5x-28=42x^2 multiply each side by 14x.
42x^2-5x+28=0
x=5/84 + sqrt(4679)/84 * i, x=5/84 - sqrt(4679)/84 * i (see below)
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 42x%5E2%2B-5x%2B28+=+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%2A42%2A28=-4679.

The discriminant -4679 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 -4679 is + or - sqrt%28+4679%29+=+68.4032162986507.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+42%2Ax%5E2%2B-5%2Ax%2B28+%29