8w^2+2w+2=3

Solution for 8w^2+2w+2=3 equation:

8w^2+2w+2=3

We move all terms to the left:

8w^2+2w+2-(3)=0

We add all the numbers together, and all the variables

8w^2+2w-1=0

a = 8; b = 2; c = -1;
Δ = b2-4ac
Δ = 22-4·8·(-1)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-6}{2*8}=\frac{-8}{16}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+6}{2*8}=\frac{4}{16}
=1/4
$