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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

3x^2+12x-1=0

a = 3; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·3·(-1)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{39}}{2*3}=\frac{-12-2\sqrt{39}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{39}}{2*3}=\frac{-12+2\sqrt{39}}{6}
$