H(x)=x2-8x+1

Solution for H(x)=x2-8x+1 equation:

(H)=H2-8H+1

We move all terms to the left:

(H)-(H2-8H+1)=0

We add all the numbers together, and all the variables

-(+H^2-8H+1)+H=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-1)·(-1)
Δ = 77
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{77}}{2*-1}=\frac{-9-\sqrt{77}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{77}}{2*-1}=\frac{-9+\sqrt{77}}{-2}
$