H(10)=x^2+6

Solution for H(10)=x^2+6 equation:

(10)=H^2+6

We move all terms to the left:

(10)-(H^2+6)=0

We get rid of parentheses

-H^2-6+10=0

We add all the numbers together, and all the variables

-1H^2+4=0

a = -1; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-1)·4
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*-1}=\frac{-4}{-2}
=+2
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*-1}=\frac{4}{-2}
=-2
$