A(s)=100s-(2s*2s)

Solution for A(s)=100s-(2s*2s) equation:

(A)=100A-(2A*2A)

We move all terms to the left:

(A)-(100A-(2A*2A))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(100A-(+2A*2A)), so:

100A-(+2A*2A)

We get rid of parentheses

100A-2A*2A

Wy multiply elements

-4A^2+100A

Back to the equation:

-(-4A^2+100A)


We get rid of parentheses

4A^2-100A+A=0

We add all the numbers together, and all the variables

4A^2-99A=0

a = 4; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·4·0
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*4}=\frac{0}{8}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*4}=\frac{198}{8}
=24+3/4
$