3w^2-2w-66=0

Solution for 3w^2-2w-66=0 equation:

3w^2-2w-66=0

a = 3; b = -2; c = -66;
Δ = b2-4ac
Δ = -22-4·3·(-66)
Δ = 796
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:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{199}}{2*3}=\frac{2-2\sqrt{199}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{199}}{2*3}=\frac{2+2\sqrt{199}}{6}
$