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

-1H^2+8H+33

Back to the equation:

-(-1H^2+8H+33)


We get rid of parentheses

1H^2-8H+H-33=0

We add all the numbers together, and all the variables

H^2-7H-33=0

a = 1; b = -7; c = -33;
Δ = b2-4ac
Δ = -72-4·1·(-33)
Δ = 181
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{181}}{2*1}=\frac{7-\sqrt{181}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{181}}{2*1}=\frac{7+\sqrt{181}}{2}
$