-16t^2+5000=t

Solution for -16t^2+5000=t equation:

-16t^2+5000=t

We move all terms to the left:

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

We add all the numbers together, and all the variables

-16t^2-1t+5000=0

a = -16; b = -1; c = +5000;
Δ = b2-4ac
Δ = -12-4·(-16)·5000
Δ = 320001
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{320001}}{2*-16}=\frac{1-\sqrt{320001}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{320001}}{2*-16}=\frac{1+\sqrt{320001}}{-32}
$