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

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

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

We move all terms to the left:

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


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 6w-2)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-144w^2)/108w^2+(-54w)/108w^2+(-18w)/108w^2+2=0

We multiply all the terms by the denominator


(-144w^2)+(-54w)+(-18w)+2*108w^2=0

Wy multiply elements

(-144w^2)+216w^2+(-54w)+(-18w)=0

We get rid of parentheses

-144w^2+216w^2-54w-18w=0

We add all the numbers together, and all the variables

72w^2-72w=0

a = 72; b = -72; c = 0;
Δ = b2-4ac
Δ = -722-4·72·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-72}{2*72}=\frac{0}{144}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+72}{2*72}=\frac{144}{144}
=1
$