0=16t^2+66t+5

Solution for 0=16t^2+66t+5 equation:

0=16t^2+66t+5

We move all terms to the left:

0-(16t^2+66t+5)=0

We add all the numbers together, and all the variables

-(16t^2+66t+5)=0

We get rid of parentheses

-16t^2-66t-5=0

a = -16; b = -66; c = -5;
Δ = b2-4ac
Δ = -662-4·(-16)·(-5)
Δ = 4036
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:

$\sqrt{\Delta}=\sqrt{4036}=\sqrt{4*1009}=\sqrt{4}*\sqrt{1009}=2\sqrt{1009}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1009}}{2*-16}=\frac{66-2\sqrt{1009}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1009}}{2*-16}=\frac{66+2\sqrt{1009}}{-32}
$