100=30w-2w^2

Solution for 100=30w-2w^2 equation:

100=30w-2w^2

We move all terms to the left:

100-(30w-2w^2)=0

We get rid of parentheses

2w^2-30w+100=0

a = 2; b = -30; c = +100;
Δ = b2-4ac
Δ = -302-4·2·100
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10}{2*2}=\frac{20}{4}
=5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10}{2*2}=\frac{40}{4}
=10
$