-4/5w-1/5=2/3w+1

Solution for -4/5w-1/5=2/3w+1 equation:

-4/5w-1/5=2/3w+1

We move all terms to the left:

-4/5w-1/5-(2/3w+1)=0


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w+1)!=0

w∈R


We get rid of parentheses

-4/5w-2/3w-1-1/5=0

We calculate fractions


(-12w)/375w^2+(-250w)/375w^2+(-3w)/375w^2-1=0

We multiply all the terms by the denominator


(-12w)+(-250w)+(-3w)-1*375w^2=0

Wy multiply elements

-375w^2+(-12w)+(-250w)+(-3w)=0

We get rid of parentheses

-375w^2-12w-250w-3w=0

We add all the numbers together, and all the variables

-375w^2-265w=0

a = -375; b = -265; c = 0;
Δ = b2-4ac
Δ = -2652-4·(-375)·0
Δ = 70225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70225}=265$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-265)-265}{2*-375}=\frac{0}{-750}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-265)+265}{2*-375}=\frac{530}{-750}
=-53/75
$