200=2w^2+9w

Solution for 200=2w^2+9w equation:

200=2w^2+9w

We move all terms to the left:

200-(2w^2+9w)=0

We get rid of parentheses

-2w^2-9w+200=0

a = -2; b = -9; c = +200;
Δ = b2-4ac
Δ = -92-4·(-2)·200
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-41}{2*-2}=\frac{-32}{-4}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+41}{2*-2}=\frac{50}{-4}
=-12+1/2
$