H(x)=-x2-6x-9

Solution for H(x)=-x2-6x-9 equation:

(H)=-H2-6H-9

We move all terms to the left:

(H)-(-H2-6H-9)=0

We add all the numbers together, and all the variables

-(-1H^2-6H-9)+H=0

We get rid of parentheses

1H^2+6H+H+9=0

We add all the numbers together, and all the variables

H^2+7H+9=0

a = 1; b = 7; c = +9;
Δ = b2-4ac
Δ = 72-4·1·9
Δ = 13
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{-(7)-\sqrt{13}}{2*1}=\frac{-7-\sqrt{13}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{13}}{2*1}=\frac{-7+\sqrt{13}}{2}
$