1000(t)=-16t^2+1700

Solution for 1000(t)=-16t^2+1700 equation:

1000(t)=-16t^2+1700

We move all terms to the left:

1000(t)-(-16t^2+1700)=0

We get rid of parentheses

16t^2+1000t-1700=0

a = 16; b = 1000; c = -1700;
Δ = b2-4ac
Δ = 10002-4·16·(-1700)
Δ = 1108800
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:

$\sqrt{\Delta}=\sqrt{1108800}=\sqrt{14400*77}=\sqrt{14400}*\sqrt{77}=120\sqrt{77}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-120\sqrt{77}}{2*16}=\frac{-1000-120\sqrt{77}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+120\sqrt{77}}{2*16}=\frac{-1000+120\sqrt{77}}{32}
$