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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(-16t^2+96t-78)=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 = 4224
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:

$\sqrt{\Delta}=\sqrt{4224}=\sqrt{64*66}=\sqrt{64}*\sqrt{66}=8\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{66}}{2*16}=\frac{96-8\sqrt{66}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{66}}{2*16}=\frac{96+8\sqrt{66}}{32}
$