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

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

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

We move all terms to the left:

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


Domain of the equation: 5w!=0

w!=0/5

w!=0

w∈R



Domain of the equation: 3w-6)!=0

w∈R


We get rid of parentheses

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

We calculate fractions


(-81w)/135w^2+5w/135w^2+5w/135w^2+6=0

We multiply all the terms by the denominator


(-81w)+5w+5w+6*135w^2=0

We add all the numbers together, and all the variables

10w+(-81w)+6*135w^2=0

Wy multiply elements

810w^2+10w+(-81w)=0

We get rid of parentheses

810w^2+10w-81w=0

We add all the numbers together, and all the variables

810w^2-71w=0

a = 810; b = -71; c = 0;
Δ = b2-4ac
Δ = -712-4·810·0
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-71}{2*810}=\frac{0}{1620}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+71}{2*810}=\frac{142}{1620}
=71/810
$