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

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

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

We move all terms to the left:

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


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



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

w∈R


We get rid of parentheses

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

We calculate fractions


(-10w)/135w^2+(-81w)/135w^2+(-10w)/135w^2+5=0

We multiply all the terms by the denominator


(-10w)+(-81w)+(-10w)+5*135w^2=0

Wy multiply elements

675w^2+(-10w)+(-81w)+(-10w)=0

We get rid of parentheses

675w^2-10w-81w-10w=0

We add all the numbers together, and all the variables

675w^2-101w=0

a = 675; b = -101; c = 0;
Δ = b2-4ac
Δ = -1012-4·675·0
Δ = 10201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10201}=101$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-101}{2*675}=\frac{0}{1350}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+101}{2*675}=\frac{202}{1350}
=101/675
$