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

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

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

We move all terms to the left:

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


Domain of the equation: 6w!=0

w!=0/6

w!=0

w∈R



Domain of the equation: 3w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


108w^2/288w^2+(-96w)/288w^2+(-96w)/288w^2-4=0

We multiply all the terms by the denominator


108w^2+(-96w)+(-96w)-4*288w^2=0

Wy multiply elements

108w^2-1152w^2+(-96w)+(-96w)=0

We get rid of parentheses

108w^2-1152w^2-96w-96w=0

We add all the numbers together, and all the variables

-1044w^2-192w=0

a = -1044; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·(-1044)·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*-1044}=\frac{0}{-2088}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*-1044}=\frac{384}{-2088}
=-16/87
$