-5/w+3=2/5w+15+1

Solution for -5/w+3=2/5w+15+1 equation:

-5/w+3=2/5w+15+1

We move all terms to the left:

-5/w+3-(2/5w+15+1)=0


Domain of the equation: w!=0

w∈R



Domain of the equation: 5w+15+1)!=0

We move all terms containing w to the left, all other terms to the right

5w+1)!=-15

w∈R


We add all the numbers together, and all the variables

-5/w-(2/5w+16)+3=0

We get rid of parentheses

-5/w-2/5w-16+3=0

We calculate fractions


(-25w)/5w^2+(-2w)/5w^2-16+3=0

We add all the numbers together, and all the variables

(-25w)/5w^2+(-2w)/5w^2-13=0

We multiply all the terms by the denominator


(-25w)+(-2w)-13*5w^2=0

Wy multiply elements

-65w^2+(-25w)+(-2w)=0

We get rid of parentheses

-65w^2-25w-2w=0

We add all the numbers together, and all the variables

-65w^2-27w=0

a = -65; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·(-65)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*-65}=\frac{0}{-130}
=0
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*-65}=\frac{54}{-130}
=-27/65
$