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

Solution for H(2)=x^2-8x+1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 8; c = +1;
Δ = b2-4ac
Δ = 82-4·(-1)·1
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{17}}{2*-1}=\frac{-8-2\sqrt{17}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{17}}{2*-1}=\frac{-8+2\sqrt{17}}{-2}
$