G(-4)=x^2+4X-1

Solution for G(-4)=x^2+4X-1 equation:

(-4)=G^2+4G-1

We move all terms to the left:

(-4)-(G^2+4G-1)=0

We add all the numbers together, and all the variables

-(G^2+4G-1)-4=0

We get rid of parentheses

-G^2-4G+1-4=0

We add all the numbers together, and all the variables

-1G^2-4G-3=0

a = -1; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·(-1)·(-3)
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{-(-4)-2}{2*-1}=\frac{2}{-2}
=-1
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*-1}=\frac{6}{-2}
=-3
$