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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 5w-6)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-250w)/375w^2+(-6w)/375w^2+(-3w)/375w^2+6=0

We multiply all the terms by the denominator


(-250w)+(-6w)+(-3w)+6*375w^2=0

Wy multiply elements

2250w^2+(-250w)+(-6w)+(-3w)=0

We get rid of parentheses

2250w^2-250w-6w-3w=0

We add all the numbers together, and all the variables

2250w^2-259w=0

a = 2250; b = -259; c = 0;
Δ = b2-4ac
Δ = -2592-4·2250·0
Δ = 67081
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{67081}=259$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-259)-259}{2*2250}=\frac{0}{4500}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-259)+259}{2*2250}=\frac{518}{4500}
=259/2250
$