-16t^2+77t+2=54

Solution for -16t^2+77t+2=54 equation:

-16t^2+77t+2=54

We move all terms to the left:

-16t^2+77t+2-(54)=0

We add all the numbers together, and all the variables

-16t^2+77t-52=0

a = -16; b = 77; c = -52;
Δ = b2-4ac
Δ = 772-4·(-16)·(-52)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-51}{2*-16}=\frac{-128}{-32}
=+4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+51}{2*-16}=\frac{-26}{-32}
=13/16
$