0=125t-16t^2-71

Solution for 0=125t-16t^2-71 equation:

0=125t-16t^2-71

We move all terms to the left:

0-(125t-16t^2-71)=0

We add all the numbers together, and all the variables

-(125t-16t^2-71)=0

We get rid of parentheses

16t^2-125t+71=0

a = 16; b = -125; c = +71;
Δ = b2-4ac
Δ = -1252-4·16·71
Δ = 11081
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{11081}}{2*16}=\frac{125-\sqrt{11081}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-125)+\sqrt{11081}}{2*16}=\frac{125+\sqrt{11081}}{32}
$