-16t^2-30t+600=0

Solution for -16t^2-30t+600=0 equation:

-16t^2-30t+600=0

a = -16; b = -30; c = +600;
Δ = b2-4ac
Δ = -302-4·(-16)·600
Δ = 39300
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:

$\sqrt{\Delta}=\sqrt{39300}=\sqrt{100*393}=\sqrt{100}*\sqrt{393}=10\sqrt{393}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-10\sqrt{393}}{2*-16}=\frac{30-10\sqrt{393}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+10\sqrt{393}}{2*-16}=\frac{30+10\sqrt{393}}{-32}
$