-16t^2+70t+1000=0

Solution for -16t^2+70t+1000=0 equation:

-16t^2+70t+1000=0

a = -16; b = 70; c = +1000;
Δ = b2-4ac
Δ = 702-4·(-16)·1000
Δ = 68900
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:

$\sqrt{\Delta}=\sqrt{68900}=\sqrt{100*689}=\sqrt{100}*\sqrt{689}=10\sqrt{689}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-10\sqrt{689}}{2*-16}=\frac{-70-10\sqrt{689}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+10\sqrt{689}}{2*-16}=\frac{-70+10\sqrt{689}}{-32}
$