8/2x-2/3x=2

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

8/2x-2/3x=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


24x/6x^2+(-4x)/6x^2-2=0

We multiply all the terms by the denominator


24x+(-4x)-2*6x^2=0

Wy multiply elements

-12x^2+24x+(-4x)=0

We get rid of parentheses

-12x^2+24x-4x=0

We add all the numbers together, and all the variables

-12x^2+20x=0

a = -12; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-12)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-12}=\frac{-40}{-24}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-12}=\frac{0}{-24}
=0
$