8/9x=6-2/3x

Solution for 8/9x=6-2/3x equation:

8/9x=6-2/3x

We move all terms to the left:

8/9x-(6-2/3x)=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

8/9x-(-2/3x+6)=0

We get rid of parentheses

8/9x+2/3x-6=0

We calculate fractions


24x/27x^2+18x/27x^2-6=0

We multiply all the terms by the denominator


24x+18x-6*27x^2=0

We add all the numbers together, and all the variables

42x-6*27x^2=0

Wy multiply elements

-162x^2+42x=0

a = -162; b = 42; c = 0;
Δ = b2-4ac
Δ = 422-4·(-162)·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-42}{2*-162}=\frac{-84}{-324}
=7/27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+42}{2*-162}=\frac{0}{-324}
=0
$