G(x)=120x-x2

Solution for G(x)=120x-x2 equation:

(G)=120G-G2

We move all terms to the left:

(G)-(120G-G2)=0

We add all the numbers together, and all the variables

-(+120G-1G^2)+G=0

We get rid of parentheses

1G^2-120G+G=0

We add all the numbers together, and all the variables

G^2-119G=0

a = 1; b = -119; c = 0;
Δ = b2-4ac
Δ = -1192-4·1·0
Δ = 14161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14161}=119$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-119)-119}{2*1}=\frac{0}{2}
=0
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+119}{2*1}=\frac{238}{2}
=119
$