H=176-16t^2

Solution for H=176-16t^2 equation:

=176-16H^2

We move all terms to the left:

-(176-16H^2)=0

We get rid of parentheses

16H^2-176=0

a = 16; b = 0; c = -176;
Δ = b2-4ac
Δ = 02-4·16·(-176)
Δ = 11264
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:

$\sqrt{\Delta}=\sqrt{11264}=\sqrt{1024*11}=\sqrt{1024}*\sqrt{11}=32\sqrt{11}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{11}}{2*16}=\frac{0-32\sqrt{11}}{32}
=-\frac{32\sqrt{11}}{32}
=-\sqrt{11}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{11}}{2*16}=\frac{0+32\sqrt{11}}{32}
=\frac{32\sqrt{11}}{32}
=\sqrt{11}
$