2w(1+w)=112

Solution for 2w(1+w)=112 equation:

2w(1+w)=112

We move all terms to the left:

2w(1+w)-(112)=0

We add all the numbers together, and all the variables

2w(w+1)-112=0

We multiply parentheses

2w^2+2w-112=0

a = 2; b = 2; c = -112;
Δ = b2-4ac
Δ = 22-4·2·(-112)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-30}{2*2}=\frac{-32}{4}
=-8
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+30}{2*2}=\frac{28}{4}
=7
$