H(x)=x^2+3G(x)=x^2-6

Solution for H(x)=x^2+3G(x)=x^2-6 equation:

(H)=H^2+3(H)=H^2-6

We move all terms to the left:

(H)-(H^2+3(H))=0

We get rid of parentheses

-H^2+H-3H=0

We add all the numbers together, and all the variables

-1H^2-2H=0

a = -1; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·(-1)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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