2/3x+-2/3=8/x+6

Solution for 2/3x+-2/3=8/x+6 equation:

2/3x+-2/3=8/x+6

We move all terms to the left:

2/3x+-2/3-(8/x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(8/x+6)-2/3=0

We get rid of parentheses

2/3x-8/x-6-2/3=0

We calculate fractions


2x/27x^2+(-216x)/27x^2+(-2x)/27x^2-6=0

We multiply all the terms by the denominator


2x+(-216x)+(-2x)-6*27x^2=0

Wy multiply elements

-162x^2+2x+(-216x)+(-2x)=0

We get rid of parentheses

-162x^2+2x-216x-2x=0

We add all the numbers together, and all the variables

-162x^2-216x=0

a = -162; b = -216; c = 0;
Δ = b2-4ac
Δ = -2162-4·(-162)·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-216}{2*-162}=\frac{0}{-324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+216}{2*-162}=\frac{432}{-324}
=-1+1/3
$