H=20+60t-16t^2

Solution for H=20+60t-16t^2 equation:

=20+60H-16H^2

We move all terms to the left:

-(20+60H-16H^2)=0

We get rid of parentheses

16H^2-60H-20=0

a = 16; b = -60; c = -20;
Δ = b2-4ac
Δ = -602-4·16·(-20)
Δ = 4880
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:

$\sqrt{\Delta}=\sqrt{4880}=\sqrt{16*305}=\sqrt{16}*\sqrt{305}=4\sqrt{305}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{305}}{2*16}=\frac{60-4\sqrt{305}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{305}}{2*16}=\frac{60+4\sqrt{305}}{32}
$