H(t)=-16t^2+64t+15

Solution for H(t)=-16t^2+64t+15 equation:

(H)=-16H^2+64H+15

We move all terms to the left:

(H)-(-16H^2+64H+15)=0

We get rid of parentheses

16H^2-64H+H-15=0

We add all the numbers together, and all the variables

16H^2-63H-15=0

a = 16; b = -63; c = -15;
Δ = b2-4ac
Δ = -632-4·16·(-15)
Δ = 4929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-\sqrt{4929}}{2*16}=\frac{63-\sqrt{4929}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{4929}}{2*16}=\frac{63+\sqrt{4929}}{32}
$