5=-16t^2+5t+54

Solution for 5=-16t^2+5t+54 equation:

5=-16t^2+5t+54

We move all terms to the left:

5-(-16t^2+5t+54)=0

We get rid of parentheses

16t^2-5t-54+5=0

We add all the numbers together, and all the variables

16t^2-5t-49=0

a = 16; b = -5; c = -49;
Δ = b2-4ac
Δ = -52-4·16·(-49)
Δ = 3161
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{-(-5)-\sqrt{3161}}{2*16}=\frac{5-\sqrt{3161}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{3161}}{2*16}=\frac{5+\sqrt{3161}}{32}
$