16=24/w+2w

Solution for 16=24/w+2w equation:

16=24/w+2w

We move all terms to the left:

16-(24/w+2w)=0


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

w∈R


We add all the numbers together, and all the variables

-(+2w+24/w)+16=0

We get rid of parentheses

-2w-24/w+16=0

We multiply all the terms by the denominator


-2w*w+16*w-24=0

We add all the numbers together, and all the variables

16w-2w*w-24=0

Wy multiply elements

-2w^2+16w-24=0

a = -2; b = 16; c = -24;
Δ = b2-4ac
Δ = 162-4·(-2)·(-24)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8}{2*-2}=\frac{-24}{-4}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8}{2*-2}=\frac{-8}{-4}
=+2
$