4/3x=2/x+3

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

4/3x=2/x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-9x^2+4x+(-6x)=0

We get rid of parentheses

-9x^2+4x-6x=0

We add all the numbers together, and all the variables

-9x^2-2x=0

a = -9; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-9)·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*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*-9}=\frac{4}{-18}
=-2/9
$