y=y(100-5y)

Solution for y=y(100-5y) equation:

y=y(100-5y)

We move all terms to the left:

y-(y(100-5y))=0

We add all the numbers together, and all the variables

y-(y(-5y+100))=0


We calculate terms in parentheses: -(y(-5y+100)), so:

y(-5y+100)

We multiply parentheses

-5y^2+100y

Back to the equation:

-(-5y^2+100y)


We get rid of parentheses

5y^2-100y+y=0

We add all the numbers together, and all the variables

5y^2-99y=0

a = 5; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·5·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*5}=\frac{0}{10}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*5}=\frac{198}{10}
=19+4/5
$