2/3x+8=4/2x

Solution for 2/3x+8=4/2x equation:

2/3x+8=4/2x

We move all terms to the left:

2/3x+8-(4/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x-(+4/2x)+8=0

We get rid of parentheses

2/3x-4/2x+8=0

We calculate fractions


4x/6x^2+(-12x)/6x^2+8=0

We multiply all the terms by the denominator


4x+(-12x)+8*6x^2=0

Wy multiply elements

48x^2+4x+(-12x)=0

We get rid of parentheses

48x^2+4x-12x=0

We add all the numbers together, and all the variables

48x^2-8x=0

a = 48; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·48·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*48}=\frac{16}{96}
=1/6
$