A=2x(4000-2x)

Solution for A=2x(4000-2x) equation:

=2A(4000-2A)

We move all terms to the left:

-(2A(4000-2A))=0

We add all the numbers together, and all the variables

-(2A(-2A+4000))=0


We calculate terms in parentheses: -(2A(-2A+4000)), so:

2A(-2A+4000)

We multiply parentheses

-4A^2+8000A

Back to the equation:

-(-4A^2+8000A)


We get rid of parentheses

4A^2-8000A=0

a = 4; b = -8000; c = 0;
Δ = b2-4ac
Δ = -80002-4·4·0
Δ = 64000000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64000000}=8000$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8000)-8000}{2*4}=\frac{0}{8}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8000)+8000}{2*4}=\frac{16000}{8}
=2000
$