5=100x(1-x)

Solution for 5=100x(1-x) equation:

5=100x(1-x)

We move all terms to the left:

5-(100x(1-x))=0

We add all the numbers together, and all the variables

-(100x(-1x+1))+5=0


We calculate terms in parentheses: -(100x(-1x+1)), so:

100x(-1x+1)

We multiply parentheses

-100x^2+100x

Back to the equation:

-(-100x^2+100x)


We get rid of parentheses

100x^2-100x+5=0

a = 100; b = -100; c = +5;
Δ = b2-4ac
Δ = -1002-4·100·5
Δ = 8000
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:

$\sqrt{\Delta}=\sqrt{8000}=\sqrt{1600*5}=\sqrt{1600}*\sqrt{5}=40\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-40\sqrt{5}}{2*100}=\frac{100-40\sqrt{5}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+40\sqrt{5}}{2*100}=\frac{100+40\sqrt{5}}{200}
$