A(x)=100x-2x2

Solution for A(x)=100x-2x2 equation:

(A)=100A-2A^2

We move all terms to the left:

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

We get rid of parentheses

2A^2-100A+A=0

We add all the numbers together, and all the variables

2A^2-99A=0

a = 2; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·2·0
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*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*2}=\frac{198}{4}
=49+1/2
$