T=-16t^2-4t+382

Solution for T=-16t^2-4t+382 equation:

=-16T^2-4T+382

We move all terms to the left:

-(-16T^2-4T+382)=0

We get rid of parentheses

16T^2+4T-382=0

a = 16; b = 4; c = -382;
Δ = b2-4ac
Δ = 42-4·16·(-382)
Δ = 24464
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:

$\sqrt{\Delta}=\sqrt{24464}=\sqrt{16*1529}=\sqrt{16}*\sqrt{1529}=4\sqrt{1529}$
$T_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{1529}}{2*16}=\frac{-4-4\sqrt{1529}}{32}
$
$T_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{1529}}{2*16}=\frac{-4+4\sqrt{1529}}{32}
$