H(t)=-3t^2-6t+11

Solution for H(t)=-3t^2-6t+11 equation:

(H)=-3H^2-6H+11

We move all terms to the left:

(H)-(-3H^2-6H+11)=0

We get rid of parentheses

3H^2+6H+H-11=0

We add all the numbers together, and all the variables

3H^2+7H-11=0

a = 3; b = 7; c = -11;
Δ = b2-4ac
Δ = 72-4·3·(-11)
Δ = 181
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{181}}{2*3}=\frac{-7-\sqrt{181}}{6}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{181}}{2*3}=\frac{-7+\sqrt{181}}{6}
$