-5/3w+4/5=-2/5w-4

Solution for -5/3w+4/5=-2/5w-4 equation:

-5/3w+4/5=-2/5w-4

We move all terms to the left:

-5/3w+4/5-(-2/5w-4)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w-4)!=0

w∈R


We get rid of parentheses

-5/3w+2/5w+4+4/5=0

We calculate fractions


(-625w)/375w^2+6w/375w^2+12w/375w^2+4=0

We multiply all the terms by the denominator


(-625w)+6w+12w+4*375w^2=0

We add all the numbers together, and all the variables

18w+(-625w)+4*375w^2=0

Wy multiply elements

1500w^2+18w+(-625w)=0

We get rid of parentheses

1500w^2+18w-625w=0

We add all the numbers together, and all the variables

1500w^2-607w=0

a = 1500; b = -607; c = 0;
Δ = b2-4ac
Δ = -6072-4·1500·0
Δ = 368449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{368449}=607$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-607)-607}{2*1500}=\frac{0}{3000}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-607)+607}{2*1500}=\frac{1214}{3000}
=607/1500
$