H(x)=(-4x-5)(-x+5)

Solution for H(x)=(-4x-5)(-x+5) equation:

(H)=(-4H-5)(-H+5)

We move all terms to the left:

(H)-((-4H-5)(-H+5))=0

We add all the numbers together, and all the variables

H-((-4H-5)(-1H+5))=0

We multiply parentheses ..

-((+4H^2-20H+5H-25))+H=0


We calculate terms in parentheses: -((+4H^2-20H+5H-25)), so:

(+4H^2-20H+5H-25)

We get rid of parentheses

4H^2-20H+5H-25

We add all the numbers together, and all the variables

4H^2-15H-25

Back to the equation:

-(4H^2-15H-25)


We add all the numbers together, and all the variables

H-(4H^2-15H-25)=0

We get rid of parentheses

-4H^2+H+15H+25=0

We add all the numbers together, and all the variables

-4H^2+16H+25=0

a = -4; b = 16; c = +25;
Δ = b2-4ac
Δ = 162-4·(-4)·25
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{41}}{2*-4}=\frac{-16-4\sqrt{41}}{-8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{41}}{2*-4}=\frac{-16+4\sqrt{41}}{-8}
$