H=-16t^2+154

Solution for H=-16t^2+154 equation:

=-16H^2+154

We move all terms to the left:

-(-16H^2+154)=0

We get rid of parentheses

16H^2-154=0

a = 16; b = 0; c = -154;
Δ = b2-4ac
Δ = 02-4·16·(-154)
Δ = 9856
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:

$\sqrt{\Delta}=\sqrt{9856}=\sqrt{64*154}=\sqrt{64}*\sqrt{154}=8\sqrt{154}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{154}}{2*16}=\frac{0-8\sqrt{154}}{32}
=-\frac{8\sqrt{154}}{32}
=-\frac{\sqrt{154}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{154}}{2*16}=\frac{0+8\sqrt{154}}{32}
=\frac{8\sqrt{154}}{32}
=\frac{\sqrt{154}}{4}
$