2/x+4/3x=2/9

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

2/x+4/3x=2/9

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-18x^2)/243x^2+486x/243x^2+324x/243x^2=0

We multiply all the terms by the denominator


(-18x^2)+486x+324x=0

We add all the numbers together, and all the variables

(-18x^2)+810x=0

We get rid of parentheses

-18x^2+810x=0

a = -18; b = 810; c = 0;
Δ = b2-4ac
Δ = 8102-4·(-18)·0
Δ = 656100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{656100}=810$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(810)-810}{2*-18}=\frac{-1620}{-36}
=+45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(810)+810}{2*-18}=\frac{0}{-36}
=0
$