H=16t(7-1t)

Solution for H=16t(7-1t) equation:

=16H(7-1H)

We move all terms to the left:

-(16H(7-1H))=0

We add all the numbers together, and all the variables

-(16H(-1H+7))=0


We calculate terms in parentheses: -(16H(-1H+7)), so:

16H(-1H+7)

We multiply parentheses

-16H^2+112H

Back to the equation:

-(-16H^2+112H)


We get rid of parentheses

16H^2-112H=0

a = 16; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·16·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*16}=\frac{0}{32}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*16}=\frac{224}{32}
=7
$