4/3x=6/4x+8

Solution for 4/3x=6/4x+8 equation:

4/3x=6/4x+8

We move all terms to the left:

4/3x-(6/4x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+8)!=0

x∈R


We get rid of parentheses

4/3x-6/4x-8=0

We calculate fractions


16x/12x^2+(-18x)/12x^2-8=0

We multiply all the terms by the denominator


16x+(-18x)-8*12x^2=0

Wy multiply elements

-96x^2+16x+(-18x)=0

We get rid of parentheses

-96x^2+16x-18x=0

We add all the numbers together, and all the variables

-96x^2-2x=0

a = -96; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-96)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-96}=\frac{4}{-192}
=-1/48
$