1/3+1/2w=1/4w-5

Solution for 1/3+1/2w=1/4w-5 equation:

1/3+1/2w=1/4w-5

We move all terms to the left:

1/3+1/2w-(1/4w-5)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 4w-5)!=0

w∈R


We get rid of parentheses

1/2w-1/4w+5+1/3=0

We calculate fractions


32w^2/72w^2+36w/72w^2+(-18w)/72w^2+5=0

We multiply all the terms by the denominator


32w^2+36w+(-18w)+5*72w^2=0

Wy multiply elements

32w^2+360w^2+36w+(-18w)=0

We get rid of parentheses

32w^2+360w^2+36w-18w=0

We add all the numbers together, and all the variables

392w^2+18w=0

a = 392; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·392·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*392}=\frac{-36}{784}
=-9/196
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*392}=\frac{0}{784}
=0
$