0=-16t^2+77t+.75

Solution for 0=-16t^2+77t+.75 equation:

0=-16t^2+77t+.75

We move all terms to the left:

0-(-16t^2+77t+.75)=0

We add all the numbers together, and all the variables

-(-16t^2+77t+.75)=0

We get rid of parentheses

16t^2-77t-.75=0

We add all the numbers together, and all the variables

16t^2-77t-0.75=0

a = 16; b = -77; c = -0.75;
Δ = b2-4ac
Δ = -772-4·16·(-0.75)
Δ = 5977
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-77)-\sqrt{5977}}{2*16}=\frac{77-\sqrt{5977}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77)+\sqrt{5977}}{2*16}=\frac{77+\sqrt{5977}}{32}
$