2170=2w^2+8w

Solution for 2170=2w^2+8w equation:

2170=2w^2+8w

We move all terms to the left:

2170-(2w^2+8w)=0

We get rid of parentheses

-2w^2-8w+2170=0

a = -2; b = -8; c = +2170;
Δ = b2-4ac
Δ = -82-4·(-2)·2170
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-132}{2*-2}=\frac{-124}{-4}
=+31
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+132}{2*-2}=\frac{140}{-4}
=-35
$