0=-16t^2+40t+271

Solution for 0=-16t^2+40t+271 equation:

0=-16t^2+40t+271

We move all terms to the left:

0-(-16t^2+40t+271)=0

We add all the numbers together, and all the variables

-(-16t^2+40t+271)=0

We get rid of parentheses

16t^2-40t-271=0

a = 16; b = -40; c = -271;
Δ = b2-4ac
Δ = -402-4·16·(-271)
Δ = 18944
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:

$\sqrt{\Delta}=\sqrt{18944}=\sqrt{256*74}=\sqrt{256}*\sqrt{74}=16\sqrt{74}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{74}}{2*16}=\frac{40-16\sqrt{74}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{74}}{2*16}=\frac{40+16\sqrt{74}}{32}
$