5=170t-16t^2

Solution for 5=170t-16t^2 equation:

5=170t-16t^2

We move all terms to the left:

5-(170t-16t^2)=0

We get rid of parentheses

16t^2-170t+5=0

a = 16; b = -170; c = +5;
Δ = b2-4ac
Δ = -1702-4·16·5
Δ = 28580
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:

$\sqrt{\Delta}=\sqrt{28580}=\sqrt{4*7145}=\sqrt{4}*\sqrt{7145}=2\sqrt{7145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{7145}}{2*16}=\frac{170-2\sqrt{7145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{7145}}{2*16}=\frac{170+2\sqrt{7145}}{32}
$