6-1/3x=x-2

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

6-1/3x=x-2

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-x*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+24x-1=0

a = -3; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·(-3)·(-1)
Δ = 564
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:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{141}}{2*-3}=\frac{-24-2\sqrt{141}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{141}}{2*-3}=\frac{-24+2\sqrt{141}}{-6}
$