H(t)=-16t^2+84t+7

Solution for H(t)=-16t^2+84t+7 equation:

(H)=-16H^2+84H+7

We move all terms to the left:

(H)-(-16H^2+84H+7)=0

We get rid of parentheses

16H^2-84H+H-7=0

We add all the numbers together, and all the variables

16H^2-83H-7=0

a = 16; b = -83; c = -7;
Δ = b2-4ac
Δ = -832-4·16·(-7)
Δ = 7337
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{-(-83)-\sqrt{7337}}{2*16}=\frac{83-\sqrt{7337}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-83)+\sqrt{7337}}{2*16}=\frac{83+\sqrt{7337}}{32}
$