2/x-4=7/3x

Solution for 2/x-4=7/3x equation:

2/x-4=7/3x

We move all terms to the left:

2/x-4-(7/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2/x-(+7/3x)-4=0

We get rid of parentheses

2/x-7/3x-4=0

We calculate fractions


6x/3x^2+(-7x)/3x^2-4=0

We multiply all the terms by the denominator


6x+(-7x)-4*3x^2=0

Wy multiply elements

-12x^2+6x+(-7x)=0

We get rid of parentheses

-12x^2+6x-7x=0

We add all the numbers together, and all the variables

-12x^2-1x=0

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

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