(2w+3)w=44

Solution for (2w+3)w=44 equation:

(2w+3)w=44

We move all terms to the left:

(2w+3)w-(44)=0

We multiply parentheses

2w^2+3w-44=0

a = 2; b = 3; c = -44;
Δ = b2-4ac
Δ = 32-4·2·(-44)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-19}{2*2}=\frac{-22}{4}
=-5+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+19}{2*2}=\frac{16}{4}
=4
$