3/2w-6/5=-1/5w-7

Solution for 3/2w-6/5=-1/5w-7 equation:

3/2w-6/5=-1/5w-7

We move all terms to the left:

3/2w-6/5-(-1/5w-7)=0


Domain of the equation: 2w!=0

w!=0/2

w!=0

w∈R



Domain of the equation: 5w-7)!=0

w∈R


We get rid of parentheses

3/2w+1/5w+7-6/5=0

We calculate fractions


375w/250w^2+2w/250w^2+(-12w)/250w^2+7=0

We multiply all the terms by the denominator


375w+2w+(-12w)+7*250w^2=0

We add all the numbers together, and all the variables

377w+(-12w)+7*250w^2=0

Wy multiply elements

1750w^2+377w+(-12w)=0

We get rid of parentheses

1750w^2+377w-12w=0

We add all the numbers together, and all the variables

1750w^2+365w=0

a = 1750; b = 365; c = 0;
Δ = b2-4ac
Δ = 3652-4·1750·0
Δ = 133225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{133225}=365$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(365)-365}{2*1750}=\frac{-730}{3500}
=-73/350
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(365)+365}{2*1750}=\frac{0}{3500}
=0
$