0.2=x(1-x)

Solution for 0.2=x(1-x) equation:

0.2=x(1-x)

We move all terms to the left:

0.2-(x(1-x))=0

We add all the numbers together, and all the variables

-(x(-1x+1))+0.2=0


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

x(-1x+1)

We multiply parentheses

-1x^2+x

Back to the equation:

-(-1x^2+x)


We get rid of parentheses

1x^2-x+0.2=0

We add all the numbers together, and all the variables

x^2-1x+0.2=0

a = 1; b = -1; c = +0.2;
Δ = b2-4ac
Δ = -12-4·1·0.2
Δ = 0.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{0.2}}{2*1}=\frac{1-\sqrt{0.2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{0.2}}{2*1}=\frac{1+\sqrt{0.2}}{2}
$