w(2w-2)=112

Solution for w(2w-2)=112 equation:

w(2w-2)=112

We move all terms to the left:

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