6w+2w^2=129

Solution for 6w+2w^2=129 equation:

6w+2w^2=129

We move all terms to the left:

6w+2w^2-(129)=0

a = 2; b = 6; c = -129;
Δ = b2-4ac
Δ = 62-4·2·(-129)
Δ = 1068
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:

$\sqrt{\Delta}=\sqrt{1068}=\sqrt{4*267}=\sqrt{4}*\sqrt{267}=2\sqrt{267}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{267}}{2*2}=\frac{-6-2\sqrt{267}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{267}}{2*2}=\frac{-6+2\sqrt{267}}{4}
$