H=173-16t^2

Solution for H=173-16t^2 equation:

=173-16H^2

We move all terms to the left:

-(173-16H^2)=0

We get rid of parentheses

16H^2-173=0

a = 16; b = 0; c = -173;
Δ = b2-4ac
Δ = 02-4·16·(-173)
Δ = 11072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11072}=\sqrt{64*173}=\sqrt{64}*\sqrt{173}=8\sqrt{173}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{173}}{2*16}=\frac{0-8\sqrt{173}}{32}
=-\frac{8\sqrt{173}}{32}
=-\frac{\sqrt{173}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{173}}{2*16}=\frac{0+8\sqrt{173}}{32}
=\frac{8\sqrt{173}}{32}
=\frac{\sqrt{173}}{4}
$