0(t)=-16t^2+64t+100

Solution for 0(t)=-16t^2+64t+100 equation:

0(t)=-16t^2+64t+100

We move all terms to the left:

0(t)-(-16t^2+64t+100)=0

We add all the numbers together, and all the variables

-(-16t^2+64t+100)+t=0

We get rid of parentheses

16t^2-64t+t-100=0

We add all the numbers together, and all the variables

16t^2-63t-100=0

a = 16; b = -63; c = -100;
Δ = b2-4ac
Δ = -632-4·16·(-100)
Δ = 10369
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{10369}}{2*16}=\frac{63-\sqrt{10369}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{10369}}{2*16}=\frac{63+\sqrt{10369}}{32}
$