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

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

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

We move all terms to the left:

-5/3w-2/5-(1/5w-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

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

We calculate fractions


(-625w)/375w^2+(-3w)/375w^2+(-6w)/375w^2+3=0

We multiply all the terms by the denominator


(-625w)+(-3w)+(-6w)+3*375w^2=0

Wy multiply elements

1125w^2+(-625w)+(-3w)+(-6w)=0

We get rid of parentheses

1125w^2-625w-3w-6w=0

We add all the numbers together, and all the variables

1125w^2-634w=0

a = 1125; b = -634; c = 0;
Δ = b2-4ac
Δ = -6342-4·1125·0
Δ = 401956
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{401956}=634$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-634)-634}{2*1125}=\frac{0}{2250}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-634)+634}{2*1125}=\frac{1268}{2250}
=634/1125
$