5=-16t^2+125t

Solution for 5=-16t^2+125t equation:

5=-16t^2+125t

We move all terms to the left:

5-(-16t^2+125t)=0

We get rid of parentheses

16t^2-125t+5=0

a = 16; b = -125; c = +5;
Δ = b2-4ac
Δ = -1252-4·16·5
Δ = 15305
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{-(-125)-\sqrt{15305}}{2*16}=\frac{125-\sqrt{15305}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+\sqrt{15305}}{2*16}=\frac{125+\sqrt{15305}}{32}
$