H=152-16t^2

Solution for H=152-16t^2 equation:

=152-16H^2

We move all terms to the left:

-(152-16H^2)=0

We get rid of parentheses

16H^2-152=0

a = 16; b = 0; c = -152;
Δ = b2-4ac
Δ = 02-4·16·(-152)
Δ = 9728
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:

$\sqrt{\Delta}=\sqrt{9728}=\sqrt{256*38}=\sqrt{256}*\sqrt{38}=16\sqrt{38}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{38}}{2*16}=\frac{0-16\sqrt{38}}{32}
=-\frac{16\sqrt{38}}{32}
=-\frac{\sqrt{38}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{38}}{2*16}=\frac{0+16\sqrt{38}}{32}
=\frac{16\sqrt{38}}{32}
=\frac{\sqrt{38}}{2}
$