2w+4w^2=66

Solution for 2w+4w^2=66 equation:

2w+4w^2=66

We move all terms to the left:

2w+4w^2-(66)=0

a = 4; b = 2; c = -66;
Δ = b2-4ac
Δ = 22-4·4·(-66)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{265}}{2*4}=\frac{-2-2\sqrt{265}}{8}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{265}}{2*4}=\frac{-2+2\sqrt{265}}{8}
$