-16t^2+384t+4=0

Solution for -16t^2+384t+4=0 equation:

-16t^2+384t+4=0

a = -16; b = 384; c = +4;
Δ = b2-4ac
Δ = 3842-4·(-16)·4
Δ = 147712
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:

$\sqrt{\Delta}=\sqrt{147712}=\sqrt{256*577}=\sqrt{256}*\sqrt{577}=16\sqrt{577}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-16\sqrt{577}}{2*-16}=\frac{-384-16\sqrt{577}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+16\sqrt{577}}{2*-16}=\frac{-384+16\sqrt{577}}{-32}
$