8/3x=4/4x-4

Solution for 8/3x=4/4x-4 equation:

8/3x=4/4x-4

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


32x/12x^2+(-12x)/12x^2+4=0

We multiply all the terms by the denominator


32x+(-12x)+4*12x^2=0

Wy multiply elements

48x^2+32x+(-12x)=0

We get rid of parentheses

48x^2+32x-12x=0

We add all the numbers together, and all the variables

48x^2+20x=0

a = 48; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·48·0
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*48}=\frac{-40}{96}
=-5/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*48}=\frac{0}{96}
=0
$