H(t)=-16t^2+12t+52

Solution for H(t)=-16t^2+12t+52 equation:

(H)=-16H^2+12H+52

We move all terms to the left:

(H)-(-16H^2+12H+52)=0

We get rid of parentheses

16H^2-12H+H-52=0

We add all the numbers together, and all the variables

16H^2-11H-52=0

a = 16; b = -11; c = -52;
Δ = b2-4ac
Δ = -112-4·16·(-52)
Δ = 3449
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{-(-11)-\sqrt{3449}}{2*16}=\frac{11-\sqrt{3449}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{3449}}{2*16}=\frac{11+\sqrt{3449}}{32}
$