3w^2+2w=72

Solution for 3w^2+2w=72 equation:

3w^2+2w=72

We move all terms to the left:

3w^2+2w-(72)=0

a = 3; b = 2; c = -72;
Δ = b2-4ac
Δ = 22-4·3·(-72)
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{217}}{2*3}=\frac{-2-2\sqrt{217}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{217}}{2*3}=\frac{-2+2\sqrt{217}}{6}
$