16=-16t^2+48t+6

Solution for 16=-16t^2+48t+6 equation:

16=-16t^2+48t+6

We move all terms to the left:

16-(-16t^2+48t+6)=0

We get rid of parentheses

16t^2-48t-6+16=0

We add all the numbers together, and all the variables

16t^2-48t+10=0

a = 16; b = -48; c = +10;
Δ = b2-4ac
Δ = -482-4·16·10
Δ = 1664
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:

$\sqrt{\Delta}=\sqrt{1664}=\sqrt{64*26}=\sqrt{64}*\sqrt{26}=8\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{26}}{2*16}=\frac{48-8\sqrt{26}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{26}}{2*16}=\frac{48+8\sqrt{26}}{32}
$