170=2w^2+4w

Solution for 170=2w^2+4w equation:

170=2w^2+4w

We move all terms to the left:

170-(2w^2+4w)=0

We get rid of parentheses

-2w^2-4w+170=0

a = -2; b = -4; c = +170;
Δ = b2-4ac
Δ = -42-4·(-2)·170
Δ = 1376
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:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{86}}{2*-2}=\frac{4-4\sqrt{86}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{86}}{2*-2}=\frac{4+4\sqrt{86}}{-4}
$