H(t)=-t^2+8t+2

Solution for H(t)=-t^2+8t+2 equation:

(H)=-H^2+8H+2

We move all terms to the left:

(H)-(-H^2+8H+2)=0

We get rid of parentheses

H^2-8H+H-2=0

We add all the numbers together, and all the variables

H^2-7H-2=0

a = 1; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·1·(-2)
Δ = 57
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{-(-7)-\sqrt{57}}{2*1}=\frac{7-\sqrt{57}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{57}}{2*1}=\frac{7+\sqrt{57}}{2}
$