8/4x=3x/2x

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

8/4x=3x/2x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

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

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


(-12x^2)+16x=0

We get rid of parentheses

-12x^2+16x=0

a = -12; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-12)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-12}=\frac{-32}{-24}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-12}=\frac{0}{-24}
=0
$