H(t)=-8t^2+60t

Solution for H(t)=-8t^2+60t equation:

(H)=-8H^2+60H

We move all terms to the left:

(H)-(-8H^2+60H)=0

We get rid of parentheses

8H^2-60H+H=0

We add all the numbers together, and all the variables

8H^2-59H=0

a = 8; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·8·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*8}=\frac{0}{16}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*8}=\frac{118}{16}
=7+3/8
$