4/x+8=2x-6/x

Solution for 4/x+8=2x-6/x equation:

4/x+8=2x-6/x

We move all terms to the left:

4/x+8-(2x-6/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-(+2x-6/x)+8=0

We get rid of parentheses

4/x-2x+6/x+8=0

We multiply all the terms by the denominator


-2x*x+8*x+4+6=0

We add all the numbers together, and all the variables

8x-2x*x+10=0

Wy multiply elements

-2x^2+8x+10=0

a = -2; b = 8; c = +10;
Δ = b2-4ac
Δ = 82-4·(-2)·10
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-12}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+12}{2*-2}=\frac{4}{-4}
=-1
$