0=5+17t-16t^2

Solution for 0=5+17t-16t^2 equation:

0=5+17t-16t^2

We move all terms to the left:

0-(5+17t-16t^2)=0

We add all the numbers together, and all the variables

-(5+17t-16t^2)=0

We get rid of parentheses

16t^2-17t-5=0

a = 16; b = -17; c = -5;
Δ = b2-4ac
Δ = -172-4·16·(-5)
Δ = 609
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{-(-17)-\sqrt{609}}{2*16}=\frac{17-\sqrt{609}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{609}}{2*16}=\frac{17+\sqrt{609}}{32}
$