A(w)=-w^2+200w

Solution for A(w)=-w^2+200w equation:

(A)=-A^2+200A

We move all terms to the left:

(A)-(-A^2+200A)=0

We get rid of parentheses

A^2-200A+A=0

We add all the numbers together, and all the variables

A^2-199A=0

a = 1; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·1·0
Δ = 39601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{39601}=199$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-199)-199}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*1}=\frac{398}{2}
=199
$