H(t)=8t(7-2t)

Solution for H(t)=8t(7-2t) equation:

(H)=8H(7-2H)

We move all terms to the left:

(H)-(8H(7-2H))=0

We add all the numbers together, and all the variables

H-(8H(-2H+7))=0


We calculate terms in parentheses: -(8H(-2H+7)), so:

8H(-2H+7)

We multiply parentheses

-16H^2+56H

Back to the equation:

-(-16H^2+56H)


We get rid of parentheses

16H^2-56H+H=0

We add all the numbers together, and all the variables

16H^2-55H=0

a = 16; b = -55; c = 0;
Δ = b2-4ac
Δ = -552-4·16·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-55}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+55}{2*16}=\frac{110}{32}
=3+7/16
$