H=155-16t^2

Solution for H=155-16t^2 equation:

=155-16H^2

We move all terms to the left:

-(155-16H^2)=0

We get rid of parentheses

16H^2-155=0

a = 16; b = 0; c = -155;
Δ = b2-4ac
Δ = 02-4·16·(-155)
Δ = 9920
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:

$\sqrt{\Delta}=\sqrt{9920}=\sqrt{64*155}=\sqrt{64}*\sqrt{155}=8\sqrt{155}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{155}}{2*16}=\frac{0-8\sqrt{155}}{32}
=-\frac{8\sqrt{155}}{32}
=-\frac{\sqrt{155}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{155}}{2*16}=\frac{0+8\sqrt{155}}{32}
=\frac{8\sqrt{155}}{32}
=\frac{\sqrt{155}}{4}
$