0=6+44(t)-16t^2

Solution for 0=6+44(t)-16t^2 equation:

0=6+44(t)-16t^2

We move all terms to the left:

0-(6+44(t)-16t^2)=0

We add all the numbers together, and all the variables

-(6+44t-16t^2)=0

We get rid of parentheses

16t^2-44t-6=0

a = 16; b = -44; c = -6;
Δ = b2-4ac
Δ = -442-4·16·(-6)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{145}}{2*16}=\frac{44-4\sqrt{145}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{145}}{2*16}=\frac{44+4\sqrt{145}}{32}
$