2*w^2+2*w=31.5

Solution for 2*w^2+2*w=31.5 equation:

2w^2+2w=31.5

We move all terms to the left:

2w^2+2w-(31.5)=0

We add all the numbers together, and all the variables

2w^2+2w-31.5=0

a = 2; b = 2; c = -31.5;
Δ = b2-4ac
Δ = 22-4·2·(-31.5)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-16}{2*2}=\frac{-18}{4}
=-4+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+16}{2*2}=\frac{14}{4}
=3+1/2
$