209=2w^2-3w

Solution for 209=2w^2-3w equation:

209=2w^2-3w

We move all terms to the left:

209-(2w^2-3w)=0

We get rid of parentheses

-2w^2+3w+209=0

a = -2; b = 3; c = +209;
Δ = b2-4ac
Δ = 32-4·(-2)·209
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{-(3)-41}{2*-2}=\frac{-44}{-4}
=+11
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+41}{2*-2}=\frac{38}{-4}
=-9+1/2
$