2/9x-1/6x=2/3+11

Solution for 2/9x-1/6x=2/3+11 equation:

2/9x-1/6x=2/3+11

We move all terms to the left:

2/9x-1/6x-(2/3+11)=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 get rid of parentheses

2/9x-1/6x-11-2/3=0

We calculate fractions


(-648x^2)/486x^2+108x/486x^2+(-81x)/486x^2-11=0

We multiply all the terms by the denominator


(-648x^2)+108x+(-81x)-11*486x^2=0

Wy multiply elements

(-648x^2)-5346x^2+108x+(-81x)=0

We get rid of parentheses

-648x^2-5346x^2+108x-81x=0

We add all the numbers together, and all the variables

-5994x^2+27x=0

a = -5994; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-5994)·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*-5994}=\frac{-54}{-11988}
=1/222
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-5994}=\frac{0}{-11988}
=0
$