-16t^2-72t+8=0

Solution for -16t^2-72t+8=0 equation:

-16t^2-72t+8=0

a = -16; b = -72; c = +8;
Δ = b2-4ac
Δ = -722-4·(-16)·8
Δ = 5696
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:

$\sqrt{\Delta}=\sqrt{5696}=\sqrt{64*89}=\sqrt{64}*\sqrt{89}=8\sqrt{89}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-8\sqrt{89}}{2*-16}=\frac{72-8\sqrt{89}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+8\sqrt{89}}{2*-16}=\frac{72+8\sqrt{89}}{-32}
$