144=(2+2w)*w

Solution for 144=(2+2w)*w equation:

144=(2+2w)*w

We move all terms to the left:

144-((2+2w)*w)=0

We add all the numbers together, and all the variables

-((2w+2)*w)+144=0


We calculate terms in parentheses: -((2w+2)*w), so:

(2w+2)*w

We multiply parentheses

2w^2+2w

Back to the equation:

-(2w^2+2w)


We get rid of parentheses

-2w^2-2w+144=0

a = -2; b = -2; c = +144;
Δ = b2-4ac
Δ = -22-4·(-2)·144
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-34}{2*-2}=\frac{-32}{-4}
=+8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+34}{2*-2}=\frac{36}{-4}
=-9
$