H=-16t2+61

Solution for H=-16t2+61 equation:

=-16H^2+61

We move all terms to the left:

-(-16H^2+61)=0

We get rid of parentheses

16H^2-61=0

a = 16; b = 0; c = -61;
Δ = b2-4ac
Δ = 02-4·16·(-61)
Δ = 3904
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:

$\sqrt{\Delta}=\sqrt{3904}=\sqrt{64*61}=\sqrt{64}*\sqrt{61}=8\sqrt{61}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{61}}{2*16}=\frac{0-8\sqrt{61}}{32}
=-\frac{8\sqrt{61}}{32}
=-\frac{\sqrt{61}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{61}}{2*16}=\frac{0+8\sqrt{61}}{32}
=\frac{8\sqrt{61}}{32}
=\frac{\sqrt{61}}{4}
$