6/4x-8=3/x

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

6/4x-8=3/x

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-32x^2+6x+(-12x)=0

We get rid of parentheses

-32x^2+6x-12x=0

We add all the numbers together, and all the variables

-32x^2-6x=0

a = -32; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-32)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-32}=\frac{12}{-64}
=-3/16
$