171=16t^2+32t

Solution for 171=16t^2+32t equation:

171=16t^2+32t

We move all terms to the left:

171-(16t^2+32t)=0

We get rid of parentheses

-16t^2-32t+171=0

a = -16; b = -32; c = +171;
Δ = b2-4ac
Δ = -322-4·(-16)·171
Δ = 11968
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:

$\sqrt{\Delta}=\sqrt{11968}=\sqrt{64*187}=\sqrt{64}*\sqrt{187}=8\sqrt{187}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{187}}{2*-16}=\frac{32-8\sqrt{187}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{187}}{2*-16}=\frac{32+8\sqrt{187}}{-32}
$