6=112+96t-16t^2

Solution for 6=112+96t-16t^2 equation:

6=112+96t-16t^2

We move all terms to the left:

6-(112+96t-16t^2)=0

We get rid of parentheses

16t^2-96t-112+6=0

We add all the numbers together, and all the variables

16t^2-96t-106=0

a = 16; b = -96; c = -106;
Δ = b2-4ac
Δ = -962-4·16·(-106)
Δ = 16000
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:

$\sqrt{\Delta}=\sqrt{16000}=\sqrt{1600*10}=\sqrt{1600}*\sqrt{10}=40\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-40\sqrt{10}}{2*16}=\frac{96-40\sqrt{10}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+40\sqrt{10}}{2*16}=\frac{96+40\sqrt{10}}{32}
$