/-16t2+48t+64=0

Solution for /-16t2+48t+64=0 equation:

/-16t^2+48t+64=0

We add all the numbers together, and all the variables

-16t^2+48t+65=0

a = -16; b = 48; c = +65;
Δ = b2-4ac
Δ = 482-4·(-16)·65
Δ = 6464
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:

$\sqrt{\Delta}=\sqrt{6464}=\sqrt{64*101}=\sqrt{64}*\sqrt{101}=8\sqrt{101}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-8\sqrt{101}}{2*-16}=\frac{-48-8\sqrt{101}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+8\sqrt{101}}{2*-16}=\frac{-48+8\sqrt{101}}{-32}
$