A(w)=-w^2+100w

Solution for A(w)=-w^2+100w equation:

(A)=-A^2+100A

We move all terms to the left:

(A)-(-A^2+100A)=0

We get rid of parentheses

A^2-100A+A=0

We add all the numbers together, and all the variables

A^2-99A=0

a = 1; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·1·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*1}=\frac{0}{2}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*1}=\frac{198}{2}
=99
$