172=96t-5t^2

Solution for 172=96t-5t^2 equation:

172=96t-5t^2

We move all terms to the left:

172-(96t-5t^2)=0

We get rid of parentheses

5t^2-96t+172=0

a = 5; b = -96; c = +172;
Δ = b2-4ac
Δ = -962-4·5·172
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-76}{2*5}=\frac{20}{10}
=2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+76}{2*5}=\frac{172}{10}
=17+1/5
$