H(t)=-6t^2+24t+14

Solution for H(t)=-6t^2+24t+14 equation:

(H)=-6H^2+24H+14

We move all terms to the left:

(H)-(-6H^2+24H+14)=0

We get rid of parentheses

6H^2-24H+H-14=0

We add all the numbers together, and all the variables

6H^2-23H-14=0

a = 6; b = -23; c = -14;
Δ = b2-4ac
Δ = -232-4·6·(-14)
Δ = 865
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{-(-23)-\sqrt{865}}{2*6}=\frac{23-\sqrt{865}}{12}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{865}}{2*6}=\frac{23+\sqrt{865}}{12}
$