H(2)=x^2-5x+7

Solution for H(2)=x^2-5x+7 equation:

(2)=H^2-5H+7

We move all terms to the left:

(2)-(H^2-5H+7)=0

We get rid of parentheses

-H^2+5H-7+2=0

We add all the numbers together, and all the variables

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

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