G(x)=x2+5x

Solution for G(x)=x2+5x equation:

(G)=G2+5G

We move all terms to the left:

(G)-(G2+5G)=0

We add all the numbers together, and all the variables

-(+G^2+5G)+G=0

We get rid of parentheses

-G^2-5G+G=0

We add all the numbers together, and all the variables

-1G^2-4G=0

a = -1; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-1)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-1}=\frac{0}{-2}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-1}=\frac{8}{-2}
=-4
$