H(x)=x2-8x

Solution for H(x)=x2-8x equation:

(H)=H2-8H

We move all terms to the left:

(H)-(H2-8H)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-H^2+8H+H=0

We add all the numbers together, and all the variables

-1H^2+9H=0

a = -1; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-1}=\frac{-18}{-2}
=+9
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-1}=\frac{0}{-2}
=0
$