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

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

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

We move all terms to the left:

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


Domain of the equation: 5w!=0

w!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


45w^2/240w^2+(-192w)/240w^2+(-80w)/240w^2+4=0

We multiply all the terms by the denominator


45w^2+(-192w)+(-80w)+4*240w^2=0

Wy multiply elements

45w^2+960w^2+(-192w)+(-80w)=0

We get rid of parentheses

45w^2+960w^2-192w-80w=0

We add all the numbers together, and all the variables

1005w^2-272w=0

a = 1005; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·1005·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*1005}=\frac{0}{2010}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*1005}=\frac{544}{2010}
=272/1005
$