x+6=8x/3x+2

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

x+6=8x/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x*3x-8x-2*3x+6*3x=0

We add all the numbers together, and all the variables

-8x+x*3x-2*3x+6*3x=0

Wy multiply elements

3x^2-8x-6x+18x=0

We add all the numbers together, and all the variables

3x^2+4x=0

a = 3; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·3·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*3}=\frac{-8}{6}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*3}=\frac{0}{6}
=0
$