9/3x=4/x+2

Solution for 9/3x=4/x+2 equation:

9/3x=4/x+2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+2)!=0

x∈R


We get rid of parentheses

9/3x-4/x-2=0

We calculate fractions


9x/3x^2+(-12x)/3x^2-2=0

We multiply all the terms by the denominator


9x+(-12x)-2*3x^2=0

Wy multiply elements

-6x^2+9x+(-12x)=0

We get rid of parentheses

-6x^2+9x-12x=0

We add all the numbers together, and all the variables

-6x^2-3x=0

a = -6; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-6)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-6}=\frac{6}{-12}
=-1/2
$