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

Solution for H(x)=-(x+1)(x-7) equation:

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

-(+H^2-7H+H-7)

We get rid of parentheses

-H^2+7H-H+7

We add all the numbers together, and all the variables

-1H^2+6H+7

Back to the equation:

-(-1H^2+6H+7)


We get rid of parentheses

1H^2-6H+H-7=0

We add all the numbers together, and all the variables

H^2-5H-7=0

a = 1; b = -5; c = -7;
Δ = b2-4ac
Δ = -52-4·1·(-7)
Δ = 53
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{-(-5)-\sqrt{53}}{2*1}=\frac{5-\sqrt{53}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{53}}{2*1}=\frac{5+\sqrt{53}}{2}
$