2w^2-4W=170

Solution for 2w^2-4W=170 equation:

2w^2-4=170

We move all terms to the left:

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

We add all the numbers together, and all the variables

2w^2-174=0

a = 2; b = 0; c = -174;
Δ = b2-4ac
Δ = 02-4·2·(-174)
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{87}}{2*2}=\frac{0-4\sqrt{87}}{4}
=-\frac{4\sqrt{87}}{4}
=-\sqrt{87}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{87}}{2*2}=\frac{0+4\sqrt{87}}{4}
=\frac{4\sqrt{87}}{4}
=\sqrt{87}
$