900=100w-w^2

Solution for 900=100w-w^2 equation:

900=100w-w^2

We move all terms to the left:

900-(100w-w^2)=0

We get rid of parentheses

w^2-100w+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:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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