-30,000+1600t-16t^2=0

Solution for -30,000+1600t-16t^2=0 equation:

-30.000+1600t-16t^2=0

We add all the numbers together, and all the variables

-16t^2+1600t-30=0

a = -16; b = 1600; c = -30;
Δ = b2-4ac
Δ = 16002-4·(-16)·(-30)
Δ = 2558080
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:

$\sqrt{\Delta}=\sqrt{2558080}=\sqrt{64*39970}=\sqrt{64}*\sqrt{39970}=8\sqrt{39970}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1600)-8\sqrt{39970}}{2*-16}=\frac{-1600-8\sqrt{39970}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1600)+8\sqrt{39970}}{2*-16}=\frac{-1600+8\sqrt{39970}}{-32}
$