3/xx2=2/3x-4

Solution for 3/xx2=2/3x-4 equation:

3/xx2=2/3x-4

We move all terms to the left:

3/xx2-(2/3x-4)=0


Domain of the equation: xx2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

3/xx2-2/3x+4=0

We calculate fractions


9x/3x^2+(-2x)/3x^2+4=0

We multiply all the terms by the denominator


9x+(-2x)+4*3x^2=0

Wy multiply elements

12x^2+9x+(-2x)=0

We get rid of parentheses

12x^2+9x-2x=0

We add all the numbers together, and all the variables

12x^2+7x=0

a = 12; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·12·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*12}=\frac{-14}{24}
=-7/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*12}=\frac{0}{24}
=0
$