x=2x(81-x)

Solution for x=2x(81-x) equation:

x=2x(81-x)

We move all terms to the left:

x-(2x(81-x))=0

We add all the numbers together, and all the variables

x-(2x(-1x+81))=0


We calculate terms in parentheses: -(2x(-1x+81)), so:

2x(-1x+81)

We multiply parentheses

-2x^2+162x

Back to the equation:

-(-2x^2+162x)


We get rid of parentheses

2x^2-162x+x=0

We add all the numbers together, and all the variables

2x^2-161x=0

a = 2; b = -161; c = 0;
Δ = b2-4ac
Δ = -1612-4·2·0
Δ = 25921
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25921}=161$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-161)-161}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-161)+161}{2*2}=\frac{322}{4}
=80+1/2
$