9/x+6=2/3x

Solution for 9/x+6=2/3x equation:

9/x+6=2/3x

We move all terms to the left:

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


Domain of the equation: 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

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

We get rid of parentheses

9/x-2/3x+6=0

We calculate fractions


27x/3x^2+(-2x)/3x^2+6=0

We multiply all the terms by the denominator


27x+(-2x)+6*3x^2=0

Wy multiply elements

18x^2+27x+(-2x)=0

We get rid of parentheses

18x^2+27x-2x=0

We add all the numbers together, and all the variables

18x^2+25x=0

a = 18; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·18·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*18}=\frac{-50}{36}
=-1+7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*18}=\frac{0}{36}
=0
$