84=3w^2+2w

Solution for 84=3w^2+2w equation:

84=3w^2+2w

We move all terms to the left:

84-(3w^2+2w)=0

We get rid of parentheses

-3w^2-2w+84=0

a = -3; b = -2; c = +84;
Δ = b2-4ac
Δ = -22-4·(-3)·84
Δ = 1012
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:

$\sqrt{\Delta}=\sqrt{1012}=\sqrt{4*253}=\sqrt{4}*\sqrt{253}=2\sqrt{253}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{253}}{2*-3}=\frac{2-2\sqrt{253}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{253}}{2*-3}=\frac{2+2\sqrt{253}}{-6}
$