H(x)=x2-4x+1

Solution for H(x)=x2-4x+1 equation:

(H)=H2-4H+1

We move all terms to the left:

(H)-(H2-4H+1)=0

We add all the numbers together, and all the variables

-(+H^2-4H+1)+H=0

We get rid of parentheses

-H^2+4H+H-1=0

We add all the numbers together, and all the variables

-1H^2+5H-1=0

a = -1; b = 5; c = -1;
Δ = b2-4ac
Δ = 52-4·(-1)·(-1)
Δ = 21
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{-(5)-\sqrt{21}}{2*-1}=\frac{-5-\sqrt{21}}{-2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{21}}{2*-1}=\frac{-5+\sqrt{21}}{-2}
$