7=100x(1-x)

Solution for 7=100x(1-x) equation:

7=100x(1-x)

We move all terms to the left:

7-(100x(1-x))=0

We add all the numbers together, and all the variables

-(100x(-1x+1))+7=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+7=0

a = 100; b = -100; c = +7;
Δ = b2-4ac
Δ = -1002-4·100·7
Δ = 7200
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:

$\sqrt{\Delta}=\sqrt{7200}=\sqrt{3600*2}=\sqrt{3600}*\sqrt{2}=60\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{2}}{2*100}=\frac{100-60\sqrt{2}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{2}}{2*100}=\frac{100+60\sqrt{2}}{200}
$