900=y(100-y)

Solution for 900=y(100-y) equation:

900=y(100-y)

We move all terms to the left:

900-(y(100-y))=0

We add all the numbers together, and all the variables

-(y(-1y+100))+900=0


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

y(-1y+100)

We multiply parentheses

-1y^2+100y

Back to the equation:

-(-1y^2+100y)


We get rid of parentheses

1y^2-100y+900=0

We add all the numbers together, and all the variables

y^2-100y+900=0

a = 1; b = -100; c = +900;
Δ = b2-4ac
Δ = -1002-4·1·900
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-80}{2*1}=\frac{20}{2}
=10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+80}{2*1}=\frac{180}{2}
=90
$