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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


1x*3x+6*3x+2*3x-1=0

Wy multiply elements

3x^2+18x+6x-1=0

We add all the numbers together, and all the variables

3x^2+24x-1=0

a = 3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·3·(-1)
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-14\sqrt{3}}{2*3}=\frac{-24-14\sqrt{3}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+14\sqrt{3}}{2*3}=\frac{-24+14\sqrt{3}}{6}
$