H(x)=-5(x+1)(x-9)

Solution for H(x)=-5(x+1)(x-9) equation:

(H)=-5(H+1)(H-9)

We move all terms to the left:

(H)-(-5(H+1)(H-9))=0

We multiply parentheses ..

-(-5(+H^2-9H+H-9))+H=0


We calculate terms in parentheses: -(-5(+H^2-9H+H-9)), so:

-5(+H^2-9H+H-9)

We multiply parentheses

-5H^2+45H-5H+45

We add all the numbers together, and all the variables

-5H^2+40H+45

Back to the equation:

-(-5H^2+40H+45)


We get rid of parentheses

5H^2-40H+H-45=0

We add all the numbers together, and all the variables

5H^2-39H-45=0

a = 5; b = -39; c = -45;
Δ = b2-4ac
Δ = -392-4·5·(-45)
Δ = 2421
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:

$\sqrt{\Delta}=\sqrt{2421}=\sqrt{9*269}=\sqrt{9}*\sqrt{269}=3\sqrt{269}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{269}}{2*5}=\frac{39-3\sqrt{269}}{10}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{269}}{2*5}=\frac{39+3\sqrt{269}}{10}
$