A(w)=18w-w^2

Solution for A(w)=18w-w^2 equation:

(A)=18A-A^2

We move all terms to the left:

(A)-(18A-A^2)=0

We get rid of parentheses

A^2-18A+A=0

We add all the numbers together, and all the variables

A^2-17A=0

a = 1; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·1·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*1}=\frac{34}{2}
=17
$