8/9x-5/6x=2/3

Solution for 8/9x-5/6x=2/3 equation:

8/9x-5/6x=2/3

We move all terms to the left:

8/9x-5/6x-(2/3)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

8/9x-5/6x-(+2/3)=0

We get rid of parentheses

8/9x-5/6x-2/3=0

We calculate fractions


(-648x^2)/486x^2+432x/486x^2+(-405x)/486x^2=0

We multiply all the terms by the denominator


(-648x^2)+432x+(-405x)=0

We get rid of parentheses

-648x^2+432x-405x=0

We add all the numbers together, and all the variables

-648x^2+27x=0

a = -648; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-648)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-648}=\frac{-54}{-1296}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-648}=\frac{0}{-1296}
=0
$