-4/5w+1/4=8/15w

Solution for -4/5w+1/4=8/15w equation:

-4/5w+1/4=8/15w

We move all terms to the left:

-4/5w+1/4-(8/15w)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 15w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

-4/5w-(+8/15w)+1/4=0

We get rid of parentheses

-4/5w-8/15w+1/4=0

We calculate fractions


75w^2/1200w^2+(-960w)/1200w^2+(-640w)/1200w^2=0

We multiply all the terms by the denominator


75w^2+(-960w)+(-640w)=0

We get rid of parentheses

75w^2-960w-640w=0

We add all the numbers together, and all the variables

75w^2-1600w=0

a = 75; b = -1600; c = 0;
Δ = b2-4ac
Δ = -16002-4·75·0
Δ = 2560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2560000}=1600$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1600)-1600}{2*75}=\frac{0}{150}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1600)+1600}{2*75}=\frac{3200}{150}
=21+1/3
$