G(x)=x2+11x

Solution for G(x)=x2+11x equation:

(G)=G2+11G

We move all terms to the left:

(G)-(G2+11G)=0

We add all the numbers together, and all the variables

-(+G^2+11G)+G=0

We get rid of parentheses

-G^2-11G+G=0

We add all the numbers together, and all the variables

-1G^2-10G=0

a = -1; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-1)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-1}=\frac{0}{-2}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-1}=\frac{20}{-2}
=-10
$