H(7)=x^2-9(7)

Solution for H(7)=x^2-9(7) equation:

(7)=H^2-9(7)

We move all terms to the left:

(7)-(H^2-9(7))=0

We get rid of parentheses

-H^2+97+7=0

We add all the numbers together, and all the variables

-1H^2+104=0

a = -1; b = 0; c = +104;
Δ = b2-4ac
Δ = 02-4·(-1)·104
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*-1}=\frac{0-4\sqrt{26}}{-2}
=-\frac{4\sqrt{26}}{-2}
=-\frac{2\sqrt{26}}{-1}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*-1}=\frac{0+4\sqrt{26}}{-2}
=\frac{4\sqrt{26}}{-2}
=\frac{2\sqrt{26}}{-1}
$