H(x)=(x-11)(x+3)

Solution for H(x)=(x-11)(x+3) equation:

(H)=(H-11)(H+3)

We move all terms to the left:

(H)-((H-11)(H+3))=0

We multiply parentheses ..

-((+H^2+3H-11H-33))+H=0


We calculate terms in parentheses: -((+H^2+3H-11H-33)), so:

(+H^2+3H-11H-33)

We get rid of parentheses

H^2+3H-11H-33

We add all the numbers together, and all the variables

H^2-8H-33

Back to the equation:

-(H^2-8H-33)


We add all the numbers together, and all the variables

H-(H^2-8H-33)=0

We get rid of parentheses

-H^2+H+8H+33=0

We add all the numbers together, and all the variables

-1H^2+9H+33=0

a = -1; b = 9; c = +33;
Δ = b2-4ac
Δ = 92-4·(-1)·33
Δ = 213
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{-(9)-\sqrt{213}}{2*-1}=\frac{-9-\sqrt{213}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{213}}{2*-1}=\frac{-9+\sqrt{213}}{-2}
$