0=5+34t-16t^2

Solution for 0=5+34t-16t^2 equation:

0=5+34t-16t^2

We move all terms to the left:

0-(5+34t-16t^2)=0

We add all the numbers together, and all the variables

-(5+34t-16t^2)=0

We get rid of parentheses

16t^2-34t-5=0

a = 16; b = -34; c = -5;
Δ = b2-4ac
Δ = -342-4·16·(-5)
Δ = 1476
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:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-6\sqrt{41}}{2*16}=\frac{34-6\sqrt{41}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+6\sqrt{41}}{2*16}=\frac{34+6\sqrt{41}}{32}
$