108=21w-w^2

Solution for 108=21w-w^2 equation:

108=21w-w^2

We move all terms to the left:

108-(21w-w^2)=0

We get rid of parentheses

w^2-21w+108=0

a = 1; b = -21; c = +108;
Δ = b2-4ac
Δ = -212-4·1·108
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*1}=\frac{18}{2}
=9
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*1}=\frac{24}{2}
=12
$