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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w-3)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


875w/375w^2+21w/375w^2+(-6w)/375w^2+3=0

We multiply all the terms by the denominator


875w+21w+(-6w)+3*375w^2=0

We add all the numbers together, and all the variables

896w+(-6w)+3*375w^2=0

Wy multiply elements

1125w^2+896w+(-6w)=0

We get rid of parentheses

1125w^2+896w-6w=0

We add all the numbers together, and all the variables

1125w^2+890w=0

a = 1125; b = 890; c = 0;
Δ = b2-4ac
Δ = 8902-4·1125·0
Δ = 792100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{792100}=890$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(890)-890}{2*1125}=\frac{-1780}{2250}
=-178/225
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(890)+890}{2*1125}=\frac{0}{2250}
=0
$