D(t)=169-16t2

Solution for D(t)=169-16t2 equation:

(D)=169-16D^2

We move all terms to the left:

(D)-(169-16D^2)=0

We get rid of parentheses

16D^2+D-169=0

a = 16; b = 1; c = -169;
Δ = b2-4ac
Δ = 12-4·16·(-169)
Δ = 10817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$D_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{10817}}{2*16}=\frac{-1-\sqrt{10817}}{32}
$
$D_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{10817}}{2*16}=\frac{-1+\sqrt{10817}}{32}
$