-16t2+44t+6=0

Solution for -16t2+44t+6=0 equation:

-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}
$