3w^2-4w-72=0

Solution for 3w^2-4w-72=0 equation:

3w^2-4w-72=0

a = 3; b = -4; c = -72;
Δ = b2-4ac
Δ = -42-4·3·(-72)
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{55}}{2*3}=\frac{4-4\sqrt{55}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{55}}{2*3}=\frac{4+4\sqrt{55}}{6}
$