-16t^2+48t-30=0

Solution for -16t^2+48t-30=0 equation:

-16t^2+48t-30=0

a = -16; b = 48; c = -30;
Δ = b2-4ac
Δ = 482-4·(-16)·(-30)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{6}}{2*-16}=\frac{-48-8\sqrt{6}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{6}}{2*-16}=\frac{-48+8\sqrt{6}}{-32}
$