H=169-16t^2

Solution for H=169-16t^2 equation:

=169-16H^2

We move all terms to the left:

-(169-16H^2)=0

We get rid of parentheses

16H^2-169=0

a = 16; b = 0; c = -169;
Δ = b2-4ac
Δ = 02-4·16·(-169)
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104}{2*16}=\frac{-104}{32}
=-3+1/4
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104}{2*16}=\frac{104}{32}
=3+1/4
$