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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-1/3x+2x+12+2=0

We multiply all the terms by the denominator


2x*3x+12*3x+2*3x-1=0

Wy multiply elements

6x^2+36x+6x-1=0

We add all the numbers together, and all the variables

6x^2+42x-1=0

a = 6; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·6·(-1)
Δ = 1788
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1788}=\sqrt{4*447}=\sqrt{4}*\sqrt{447}=2\sqrt{447}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{447}}{2*6}=\frac{-42-2\sqrt{447}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{447}}{2*6}=\frac{-42+2\sqrt{447}}{12}
$