H=1t(7-t)

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

=1H(7-H)

We move all terms to the left:

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

We add all the numbers together, and all the variables

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


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

1H(-1H+7)

We multiply parentheses

-1H^2+7H

Back to the equation:

-(-1H^2+7H)


We get rid of parentheses

1H^2-7H=0

We add all the numbers together, and all the variables

H^2-7H=0

a = 1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·1·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*1}=\frac{0}{2}
=0
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*1}=\frac{14}{2}
=7
$