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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


12x^2/72x^2+108x^2/72x^2+24x/72x^2-2=0

We multiply all the terms by the denominator


12x^2+108x^2+24x-2*72x^2=0

We add all the numbers together, and all the variables

120x^2+24x-2*72x^2=0

Wy multiply elements

120x^2-144x^2+24x=0

We add all the numbers together, and all the variables

-24x^2+24x=0

a = -24; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-24)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-24}=\frac{-48}{-48}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-24}=\frac{0}{-48}
=0
$