H=-16t2+1450

Solution for H=-16t2+1450 equation:

=-16H^2+1450

We move all terms to the left:

-(-16H^2+1450)=0

We get rid of parentheses

16H^2-1450=0

a = 16; b = 0; c = -1450;
Δ = b2-4ac
Δ = 02-4·16·(-1450)
Δ = 92800
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:

$\sqrt{\Delta}=\sqrt{92800}=\sqrt{1600*58}=\sqrt{1600}*\sqrt{58}=40\sqrt{58}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{58}}{2*16}=\frac{0-40\sqrt{58}}{32}
=-\frac{40\sqrt{58}}{32}
=-\frac{5\sqrt{58}}{4}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{58}}{2*16}=\frac{0+40\sqrt{58}}{32}
=\frac{40\sqrt{58}}{32}
=\frac{5\sqrt{58}}{4}
$