-16t^2+315t+1000=0

Solution for -16t^2+315t+1000=0 equation:

-16t^2+315t+1000=0

a = -16; b = 315; c = +1000;
Δ = b2-4ac
Δ = 3152-4·(-16)·1000
Δ = 163225
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:

$\sqrt{\Delta}=\sqrt{163225}=\sqrt{25*6529}=\sqrt{25}*\sqrt{6529}=5\sqrt{6529}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-5\sqrt{6529}}{2*-16}=\frac{-315-5\sqrt{6529}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+5\sqrt{6529}}{2*-16}=\frac{-315+5\sqrt{6529}}{-32}
$