30/(4+2w)=w

Solution for 30/(4+2w)=w equation:

30/(4+2w)=w

We move all terms to the left:

30/(4+2w)-(w)=0


Domain of the equation: (4+2w)!=0

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

2w!=-4

w!=-4/2

w!=-2

w∈R


We add all the numbers together, and all the variables

30/(2w+4)-w=0

We add all the numbers together, and all the variables

-1w+30/(2w+4)=0

We multiply all the terms by the denominator


-1w*(2w+4)+30=0

We multiply parentheses

-2w^2-4w+30=0

a = -2; b = -4; c = +30;
Δ = b2-4ac
Δ = -42-4·(-2)·30
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*-2}=\frac{-12}{-4}
=+3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*-2}=\frac{20}{-4}
=-5
$