0(t)=196-16t^2

Solution for 0(t)=196-16t^2 equation:

0(t)=196-16t^2

We move all terms to the left:

0(t)-(196-16t^2)=0

We add all the numbers together, and all the variables

-(196-16t^2)+t=0

We get rid of parentheses

16t^2+t-196=0

a = 16; b = 1; c = -196;
Δ = b2-4ac
Δ = 12-4·16·(-196)
Δ = 12545
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{-(1)-\sqrt{12545}}{2*16}=\frac{-1-\sqrt{12545}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{12545}}{2*16}=\frac{-1+\sqrt{12545}}{32}
$