A(x)=x(400-2x)

Solution for A(x)=x(400-2x) equation:

(A)=A(400-2A)

We move all terms to the left:

(A)-(A(400-2A))=0

We add all the numbers together, and all the variables

A-(A(-2A+400))=0


We calculate terms in parentheses: -(A(-2A+400)), so:

A(-2A+400)

We multiply parentheses

-2A^2+400A

Back to the equation:

-(-2A^2+400A)


We get rid of parentheses

2A^2-400A+A=0

We add all the numbers together, and all the variables

2A^2-399A=0

a = 2; b = -399; c = 0;
Δ = b2-4ac
Δ = -3992-4·2·0
Δ = 159201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{159201}=399$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-399)-399}{2*2}=\frac{0}{4}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-399)+399}{2*2}=\frac{798}{4}
=199+1/2
$