-16t^2-108t+520=0

Solution for -16t^2-108t+520=0 equation:

-16t^2-108t+520=0

a = -16; b = -108; c = +520;
Δ = b2-4ac
Δ = -1082-4·(-16)·520
Δ = 44944
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{44944}=212$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-212}{2*-16}=\frac{-104}{-32}
=3+1/4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+212}{2*-16}=\frac{320}{-32}
=-10
$