200=100x(x-5/5)

Solution for 200=100x(x-5/5) equation:

200=100x(x-5/5)

We move all terms to the left:

200-(100x(x-5/5))=0

We add all the numbers together, and all the variables

-(100x(x-1))+200=0


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

100x(x-1)

We multiply parentheses

100x^2-100x

Back to the equation:

-(100x^2-100x)


We get rid of parentheses

-100x^2+100x+200=0

a = -100; b = 100; c = +200;
Δ = b2-4ac
Δ = 1002-4·(-100)·200
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-300}{2*-100}=\frac{-400}{-200}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+300}{2*-100}=\frac{200}{-200}
=-1
$