0=w^2+2w-112

Solution for 0=w^2+2w-112 equation:

0=w^2+2w-112

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-w^2-2w+112=0

We add all the numbers together, and all the variables

-1w^2-2w+112=0

a = -1; b = -2; c = +112;
Δ = b2-4ac
Δ = -22-4·(-1)·112
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{113}}{2*-1}=\frac{2-2\sqrt{113}}{-2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{113}}{2*-1}=\frac{2+2\sqrt{113}}{-2}
$