H(-1)=x2-8x+1

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

(-1)=H2-8H+1

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = 8; c = -2;
Δ = b2-4ac
Δ = 82-4·(-1)·(-2)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{14}}{2*-1}=\frac{-8-2\sqrt{14}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{14}}{2*-1}=\frac{-8+2\sqrt{14}}{-2}
$