G(-1)=x2-2

Solution for G(-1)=x2-2 equation:

(-1)=G2-2

We move all terms to the left:

(-1)-(G2-2)=0

We add all the numbers together, and all the variables

-(+G^2-2)+(-1)=0

We add all the numbers together, and all the variables

-(+G^2-2)-1=0

We get rid of parentheses

-G^2+2-1=0

We add all the numbers together, and all the variables

-1G^2+1=0

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

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