0=-16t2+59t+5

Solution for 0=-16t2+59t+5 equation:

0=-16t^2+59t+5

We move all terms to the left:

0-(-16t^2+59t+5)=0

We add all the numbers together, and all the variables

-(-16t^2+59t+5)=0

We get rid of parentheses

16t^2-59t-5=0

a = 16; b = -59; c = -5;
Δ = b2-4ac
Δ = -592-4·16·(-5)
Δ = 3801
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{-(-59)-\sqrt{3801}}{2*16}=\frac{59-\sqrt{3801}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{3801}}{2*16}=\frac{59+\sqrt{3801}}{32}
$