0=-16t^2-54t+7

Solution for 0=-16t^2-54t+7 equation:

0=-16t^2-54t+7

We move all terms to the left:

0-(-16t^2-54t+7)=0

We add all the numbers together, and all the variables

-(-16t^2-54t+7)=0

We get rid of parentheses

16t^2+54t-7=0

a = 16; b = 54; c = -7;
Δ = b2-4ac
Δ = 542-4·16·(-7)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-58}{2*16}=\frac{-112}{32}
=-3+1/2
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+58}{2*16}=\frac{4}{32}
=1/8
$