4w=27/w

Solution for 4w=27/w equation:

4w=27/w

We move all terms to the left:

4w-(27/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

4w-(+27/w)=0

We get rid of parentheses

4w-27/w=0

We multiply all the terms by the denominator


4w*w-27=0

Wy multiply elements

4w^2-27=0

a = 4; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·4·(-27)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*4}=\frac{0-12\sqrt{3}}{8}
=-\frac{12\sqrt{3}}{8}
=-\frac{3\sqrt{3}}{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*4}=\frac{0+12\sqrt{3}}{8}
=\frac{12\sqrt{3}}{8}
=\frac{3\sqrt{3}}{2}
$