H=144+-16t2

Solution for H=144+-16t2 equation:

=144+-16H^2

We move all terms to the left:

-(144+-16H^2)=0

We use the square of the difference formula

-(144-16H^2)=0

We get rid of parentheses

16H^2-144=0

a = 16; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·16·(-144)
Δ = 9216
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9216}=96$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-96}{2*16}=\frac{-96}{32}
=-3
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+96}{2*16}=\frac{96}{32}
=3
$