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

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

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

We move all terms to the left:

-1/6x+2/3x+2-(11)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


(-3x)/18x^2+12x/18x^2-9=0

We multiply all the terms by the denominator


(-3x)+12x-9*18x^2=0

We add all the numbers together, and all the variables

12x+(-3x)-9*18x^2=0

Wy multiply elements

-162x^2+12x+(-3x)=0

We get rid of parentheses

-162x^2+12x-3x=0

We add all the numbers together, and all the variables

-162x^2+9x=0

a = -162; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-162)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-162}=\frac{-18}{-324}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-162}=\frac{0}{-324}
=0
$