112=2w^2+36w

Solution for 112=2w^2+36w equation:

112=2w^2+36w

We move all terms to the left:

112-(2w^2+36w)=0

We get rid of parentheses

-2w^2-36w+112=0

a = -2; b = -36; c = +112;
Δ = b2-4ac
Δ = -362-4·(-2)·112
Δ = 2192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2192}=\sqrt{16*137}=\sqrt{16}*\sqrt{137}=4\sqrt{137}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{137}}{2*-2}=\frac{36-4\sqrt{137}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{137}}{2*-2}=\frac{36+4\sqrt{137}}{-4}
$