(w-1)(w-5)=21

Solution for (w-1)(w-5)=21 equation:

(w-1)(w-5)=21

We move all terms to the left:

(w-1)(w-5)-(21)=0

We multiply parentheses ..

(+w^2-5w-1w+5)-21=0

We get rid of parentheses

w^2-5w-1w+5-21=0

We add all the numbers together, and all the variables

w^2-6w-16=0

a = 1; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·1·(-16)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-10}{2*1}=\frac{-4}{2}
=-2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+10}{2*1}=\frac{16}{2}
=8
$