(w^2-6w-27)/(w^2+6w+5)=0

Solution for (w^2-6w-27)/(w^2+6w+5)=0 equation:

(w^2-6w-27)/(w^2+6w+5)=0


Domain of the equation: (w^2+6w+5)!=0

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

w^2+6w!=-5

w∈R


We multiply all the terms by the denominator


(w^2-6w-27)=0

We get rid of parentheses

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