A(x)=x(200-3x)

Solution for A(x)=x(200-3x) equation:

(A)=A(200-3A)

We move all terms to the left:

(A)-(A(200-3A))=0

We add all the numbers together, and all the variables

A-(A(-3A+200))=0


We calculate terms in parentheses: -(A(-3A+200)), so:

A(-3A+200)

We multiply parentheses

-3A^2+200A

Back to the equation:

-(-3A^2+200A)


We get rid of parentheses

3A^2-200A+A=0

We add all the numbers together, and all the variables

3A^2-199A=0

a = 3; b = -199; c = 0;
Δ = b2-4ac
Δ = -1992-4·3·0
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*3}=\frac{0}{6}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-199)+199}{2*3}=\frac{398}{6}
=66+1/3
$