H(t)=-5t^2+8t+1,8

Solution for H(t)=-5t^2+8t+1,8 equation:

(H)=-5H^2+8H+1.8

We move all terms to the left:

(H)-(-5H^2+8H+1.8)=0

We get rid of parentheses

5H^2-8H+H-1.8=0

We add all the numbers together, and all the variables

5H^2-7H-1.8=0

a = 5; b = -7; c = -1.8;
Δ = b2-4ac
Δ = -72-4·5·(-1.8)
Δ = 85
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{85}}{2*5}=\frac{7-\sqrt{85}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{85}}{2*5}=\frac{7+\sqrt{85}}{10}
$