2w^2+8w=52

Solution for 2w^2+8w=52 equation:

2w^2+8w=52

We move all terms to the left:

2w^2+8w-(52)=0

a = 2; b = 8; c = -52;
Δ = b2-4ac
Δ = 82-4·2·(-52)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{30}}{2*2}=\frac{-8-4\sqrt{30}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{30}}{2*2}=\frac{-8+4\sqrt{30}}{4}
$