H(t)=-16t2+48t+4

Solution for H(t)=-16t2+48t+4 equation:

(H)=-16H^2+48H+4

We move all terms to the left:

(H)-(-16H^2+48H+4)=0

We get rid of parentheses

16H^2-48H+H-4=0

We add all the numbers together, and all the variables

16H^2-47H-4=0

a = 16; b = -47; c = -4;
Δ = b2-4ac
Δ = -472-4·16·(-4)
Δ = 2465
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{-(-47)-\sqrt{2465}}{2*16}=\frac{47-\sqrt{2465}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{2465}}{2*16}=\frac{47+\sqrt{2465}}{32}
$