(2w-3)*w=209

Solution for (2w-3)*w=209 equation:

(2w-3)*w=209

We move all terms to the left:

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

We multiply 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{-38}{4}
=-9+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+41}{2*2}=\frac{44}{4}
=11
$