5/3x+6=2/9x

Solution for 5/3x+6=2/9x equation:

5/3x+6=2/9x

We move all terms to the left:

5/3x+6-(2/9x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(+2/9x)+6=0

We get rid of parentheses

5/3x-2/9x+6=0

We calculate fractions


45x/27x^2+(-6x)/27x^2+6=0

We multiply all the terms by the denominator


45x+(-6x)+6*27x^2=0

Wy multiply elements

162x^2+45x+(-6x)=0

We get rid of parentheses

162x^2+45x-6x=0

We add all the numbers together, and all the variables

162x^2+39x=0

a = 162; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·162·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*162}=\frac{-78}{324}
=-13/54
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*162}=\frac{0}{324}
=0
$