0=78+96t-16t^2

Solution for 0=78+96t-16t^2 equation:

0=78+96t-16t^2

We move all terms to the left:

0-(78+96t-16t^2)=0

We add all the numbers together, and all the variables

-(78+96t-16t^2)=0

We get rid of parentheses

16t^2-96t-78=0

a = 16; b = -96; c = -78;
Δ = b2-4ac
Δ = -962-4·16·(-78)
Δ = 14208
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:

$\sqrt{\Delta}=\sqrt{14208}=\sqrt{64*222}=\sqrt{64}*\sqrt{222}=8\sqrt{222}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{222}}{2*16}=\frac{96-8\sqrt{222}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{222}}{2*16}=\frac{96+8\sqrt{222}}{32}
$