-16t^2+20t=-1000

Solution for -16t^2+20t=-1000 equation:

-16t^2+20t=-1000

We move all terms to the left:

-16t^2+20t-(-1000)=0

We add all the numbers together, and all the variables

-16t^2+20t+1000=0

a = -16; b = 20; c = +1000;
Δ = b2-4ac
Δ = 202-4·(-16)·1000
Δ = 64400
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:

$\sqrt{\Delta}=\sqrt{64400}=\sqrt{400*161}=\sqrt{400}*\sqrt{161}=20\sqrt{161}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{161}}{2*-16}=\frac{-20-20\sqrt{161}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{161}}{2*-16}=\frac{-20+20\sqrt{161}}{-32}
$