8+5/9x=6+1/3x

Solution for 8+5/9x=6+1/3x equation:

8+5/9x=6+1/3x

We move all terms to the left:

8+5/9x-(6+1/3x)=0


Domain of the equation: 9x!=0

x!=0/9

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

5/9x-(1/3x+6)+8=0

We get rid of parentheses

5/9x-1/3x-6+8=0

We calculate fractions


15x/27x^2+(-9x)/27x^2-6+8=0

We add all the numbers together, and all the variables

15x/27x^2+(-9x)/27x^2+2=0

We multiply all the terms by the denominator


15x+(-9x)+2*27x^2=0

Wy multiply elements

54x^2+15x+(-9x)=0

We get rid of parentheses

54x^2+15x-9x=0

We add all the numbers together, and all the variables

54x^2+6x=0

a = 54; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·54·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*54}=\frac{-12}{108}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*54}=\frac{0}{108}
=0
$