H(t)=6+15t-16t^2

Solution for H(t)=6+15t-16t^2 equation:

(H)=6+15H-16H^2

We move all terms to the left:

(H)-(6+15H-16H^2)=0

We get rid of parentheses

16H^2-15H+H-6=0

We add all the numbers together, and all the variables

16H^2-14H-6=0

a = 16; b = -14; c = -6;
Δ = b2-4ac
Δ = -142-4·16·(-6)
Δ = 580
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{145}}{2*16}=\frac{14-2\sqrt{145}}{32}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{145}}{2*16}=\frac{14+2\sqrt{145}}{32}
$