2/x=1/3x+9

Solution for 2/x=1/3x+9 equation:

2/x=1/3x+9

We move all terms to the left:

2/x-(1/3x+9)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+9)!=0

x∈R


We get rid of parentheses

2/x-1/3x-9=0

We calculate fractions


6x/3x^2+(-x)/3x^2-9=0

We add all the numbers together, and all the variables

6x/3x^2+(-1x)/3x^2-9=0

We multiply all the terms by the denominator


6x+(-1x)-9*3x^2=0

Wy multiply elements

-27x^2+6x+(-1x)=0

We get rid of parentheses

-27x^2+6x-1x=0

We add all the numbers together, and all the variables

-27x^2+5x=0

a = -27; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-27)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-27}=\frac{-10}{-54}
=5/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-27}=\frac{0}{-54}
=0
$