6=w-27/w

Solution for 6=w-27/w equation:

6=w-27/w

We move all terms to the left:

6-(w-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

-(+w-27/w)+6=0

We get rid of parentheses

-w+27/w+6=0

We multiply all the terms by the denominator


-w*w+6*w+27=0

We add all the numbers together, and all the variables

6w-w*w+27=0

Wy multiply elements

-1w^2+6w+27=0

a = -1; b = 6; c = +27;
Δ = b2-4ac
Δ = 62-4·(-1)·27
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-1}=\frac{-18}{-2}
=+9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-1}=\frac{6}{-2}
=-3
$