3t^2-24t-72=0

Solution for 3t^2-24t-72=0 equation:

3t^2-24t-72=0

a = 3; b = -24; c = -72;
Δ = b2-4ac
Δ = -242-4·3·(-72)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{10}}{2*3}=\frac{24-12\sqrt{10}}{6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{10}}{2*3}=\frac{24+12\sqrt{10}}{6}
$