8w=120/w

Solution for 8w=120/w equation:

8w=120/w

We move all terms to the left:

8w-(120/w)=0


Domain of the equation: w)!=0

w!=0/1

w!=0

w∈R


We add all the numbers together, and all the variables

8w-(+120/w)=0

We get rid of parentheses

8w-120/w=0

We multiply all the terms by the denominator


8w*w-120=0

Wy multiply elements

8w^2-120=0

a = 8; b = 0; c = -120;
Δ = b2-4ac
Δ = 02-4·8·(-120)
Δ = 3840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3840}=\sqrt{256*15}=\sqrt{256}*\sqrt{15}=16\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{15}}{2*8}=\frac{0-16\sqrt{15}}{16}
=-\frac{16\sqrt{15}}{16}
=-\sqrt{15}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{15}}{2*8}=\frac{0+16\sqrt{15}}{16}
=\frac{16\sqrt{15}}{16}
=\sqrt{15}
$