4000=5000-16t2

Solution for 4000=5000-16t2 equation:

4000=5000-16t^2

We move all terms to the left:

4000-(5000-16t^2)=0

We get rid of parentheses

16t^2-5000+4000=0

We add all the numbers together, and all the variables

16t^2-1000=0

a = 16; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·16·(-1000)
Δ = 64000
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:

$\sqrt{\Delta}=\sqrt{64000}=\sqrt{6400*10}=\sqrt{6400}*\sqrt{10}=80\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80\sqrt{10}}{2*16}=\frac{0-80\sqrt{10}}{32}
=-\frac{80\sqrt{10}}{32}
=-\frac{5\sqrt{10}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80\sqrt{10}}{2*16}=\frac{0+80\sqrt{10}}{32}
=\frac{80\sqrt{10}}{32}
=\frac{5\sqrt{10}}{2}
$