0=-16t^2-44t+5

Solution for 0=-16t^2-44t+5 equation:

0=-16t^2-44t+5

We move all terms to the left:

0-(-16t^2-44t+5)=0

We add all the numbers together, and all the variables

-(-16t^2-44t+5)=0

We get rid of parentheses

16t^2+44t-5=0

a = 16; b = 44; c = -5;
Δ = b2-4ac
Δ = 442-4·16·(-5)
Δ = 2256
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:

$\sqrt{\Delta}=\sqrt{2256}=\sqrt{16*141}=\sqrt{16}*\sqrt{141}=4\sqrt{141}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{141}}{2*16}=\frac{-44-4\sqrt{141}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{141}}{2*16}=\frac{-44+4\sqrt{141}}{32}
$