H=5+60t-16t2

Solution for H=5+60t-16t2 equation:

=5+60H-16H^2

We move all terms to the left:

-(5+60H-16H^2)=0

We get rid of parentheses

16H^2-60H-5=0

a = 16; b = -60; c = -5;
Δ = b2-4ac
Δ = -602-4·16·(-5)
Δ = 3920
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:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-28\sqrt{5}}{2*16}=\frac{60-28\sqrt{5}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+28\sqrt{5}}{2*16}=\frac{60+28\sqrt{5}}{32}
$