2/3w-1/6=-1/2w+4

Solution for 2/3w-1/6=-1/2w+4 equation:

2/3w-1/6=-1/2w+4

We move all terms to the left:

2/3w-1/6-(-1/2w+4)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 2w+4)!=0

w∈R


We get rid of parentheses

2/3w+1/2w-4-1/6=0

We calculate fractions


(-12w^2)/216w^2+144w/216w^2+108w/216w^2-4=0

We multiply all the terms by the denominator


(-12w^2)+144w+108w-4*216w^2=0

We add all the numbers together, and all the variables

(-12w^2)+252w-4*216w^2=0

Wy multiply elements

(-12w^2)-864w^2+252w=0

We get rid of parentheses

-12w^2-864w^2+252w=0

We add all the numbers together, and all the variables

-876w^2+252w=0

a = -876; b = 252; c = 0;
Δ = b2-4ac
Δ = 2522-4·(-876)·0
Δ = 63504
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{63504}=252$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(252)-252}{2*-876}=\frac{-504}{-1752}
=21/73
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(252)+252}{2*-876}=\frac{0}{-1752}
=0
$