2w^2+8w=270

Solution for 2w^2+8w=270 equation:

2w^2+8w=270

We move all terms to the left:

2w^2+8w-(270)=0

a = 2; b = 8; c = -270;
Δ = b2-4ac
Δ = 82-4·2·(-270)
Δ = 2224
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:

$\sqrt{\Delta}=\sqrt{2224}=\sqrt{16*139}=\sqrt{16}*\sqrt{139}=4\sqrt{139}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{139}}{2*2}=\frac{-8-4\sqrt{139}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{139}}{2*2}=\frac{-8+4\sqrt{139}}{4}
$