H(t)=-16t^2+87t+4

Solution for H(t)=-16t^2+87t+4 equation:

(H)=-16H^2+87H+4

We move all terms to the left:

(H)-(-16H^2+87H+4)=0

We get rid of parentheses

16H^2-87H+H-4=0

We add all the numbers together, and all the variables

16H^2-86H-4=0

a = 16; b = -86; c = -4;
Δ = b2-4ac
Δ = -862-4·16·(-4)
Δ = 7652
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:

$\sqrt{\Delta}=\sqrt{7652}=\sqrt{4*1913}=\sqrt{4}*\sqrt{1913}=2\sqrt{1913}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{1913}}{2*16}=\frac{86-2\sqrt{1913}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{1913}}{2*16}=\frac{86+2\sqrt{1913}}{32}
$