G(x)=x(x+3)

Solution for G(x)=x(x+3) equation:

(G)=G(G+3)

We move all terms to the left:

(G)-(G(G+3))=0


We calculate terms in parentheses: -(G(G+3)), so:

G(G+3)

We multiply parentheses

G^2+3G

Back to the equation:

-(G^2+3G)


We get rid of parentheses

-G^2+G-3G=0

We add all the numbers together, and all the variables

-1G^2-2G=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:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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