H(x)=x^2+10x+9

Solution for H(x)=x^2+10x+9 equation:

(H)=H^2+10H+9

We move all terms to the left:

(H)-(H^2+10H+9)=0

We get rid of parentheses

-H^2+H-10H-9=0

We add all the numbers together, and all the variables

-1H^2-9H-9=0

a = -1; b = -9; c = -9;
Δ = b2-4ac
Δ = -92-4·(-1)·(-9)
Δ = 45
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{45}=\sqrt{9*5}=\sqrt{9}*\sqrt{5}=3\sqrt{5}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{5}}{2*-1}=\frac{9-3\sqrt{5}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{5}}{2*-1}=\frac{9+3\sqrt{5}}{-2}
$