(11/x)+(10/3x)=2/9

Solution for (11/x)+(10/3x)=2/9 equation:

(11/x)+(10/3x)=2/9

We move all terms to the left:

(11/x)+(10/3x)-(2/9)=0


Domain of the equation: x)!=0

x!=0/1

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

(+11/x)+(+10/3x)-(+2/9)=0

We get rid of parentheses

11/x+10/3x-2/9=0

We calculate fractions


(-18x^2)/243x^2+2673x/243x^2+810x/243x^2=0

We multiply all the terms by the denominator


(-18x^2)+2673x+810x=0

We add all the numbers together, and all the variables

(-18x^2)+3483x=0

We get rid of parentheses

-18x^2+3483x=0

a = -18; b = 3483; c = 0;
Δ = b2-4ac
Δ = 34832-4·(-18)·0
Δ = 12131289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12131289}=3483$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3483)-3483}{2*-18}=\frac{-6966}{-36}
=193+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3483)+3483}{2*-18}=\frac{0}{-36}
=0
$