-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 = 35225
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:

$\sqrt{\Delta}=\sqrt{35225}=\sqrt{25*1409}=\sqrt{25}*\sqrt{1409}=5\sqrt{1409}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-5\sqrt{1409}}{2*-16}=\frac{-315-5\sqrt{1409}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+5\sqrt{1409}}{2*-16}=\frac{-315+5\sqrt{1409}}{-32}
$