t=-16t^2+64t+5

Solution for t=-16t^2+64t+5 equation:

t=-16t^2+64t+5

We move all terms to the left:

t-(-16t^2+64t+5)=0

We get rid of parentheses

16t^2-64t+t-5=0

We add all the numbers together, and all the variables

16t^2-63t-5=0

a = 16; b = -63; c = -5;
Δ = b2-4ac
Δ = -632-4·16·(-5)
Δ = 4289
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{-(-63)-\sqrt{4289}}{2*16}=\frac{63-\sqrt{4289}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4289}}{2*16}=\frac{63+\sqrt{4289}}{32}
$