-3w^2+8w+24=0

Solution for -3w^2+8w+24=0 equation:

-3w^2+8w+24=0

a = -3; b = 8; c = +24;
Δ = b2-4ac
Δ = 82-4·(-3)·24
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*-3}=\frac{-8-4\sqrt{22}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*-3}=\frac{-8+4\sqrt{22}}{-6}
$