3t^2-8t-24=0

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

3t^2-8t-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:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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