20*x*(1-x)=1

Solution for 20*x*(1-x)=1 equation:

20x(1-x)=1

We move all terms to the left:

20x(1-x)-(1)=0

We add all the numbers together, and all the variables

20x(-1x+1)-1=0

We multiply parentheses

-20x^2+20x-1=0

a = -20; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-20)·(-1)
Δ = 320
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{5}}{2*-20}=\frac{-20-8\sqrt{5}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{5}}{2*-20}=\frac{-20+8\sqrt{5}}{-40}
$