0=23w-w^2-132

Solution for 0=23w-w^2-132 equation:

0=23w-w^2-132

We move all terms to the left:

0-(23w-w^2-132)=0

We add all the numbers together, and all the variables

-(23w-w^2-132)=0

We get rid of parentheses

w^2-23w+132=0

a = 1; b = -23; c = +132;
Δ = b2-4ac
Δ = -232-4·1·132
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-1}{2*1}=\frac{22}{2}
=11
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+1}{2*1}=\frac{24}{2}
=12
$