G(x)=1/2x-4.5+6.6

Solution for G(x)=1/2x-4.5+6.6 equation:

(G)=1/2G-4.5+6.6

We move all terms to the left:

(G)-(1/2G-4.5+6.6)=0


Domain of the equation: 2G-4.5+6.6)!=0

We move all terms containing G to the left, all other terms to the right

2G+6.6)!=4.5

G∈R


We add all the numbers together, and all the variables

G-(1/2G+2.1)=0

We get rid of parentheses

G-1/2G-2.1=0

We multiply all the terms by the denominator


G*2G-(2.1)*2G-1=0

We multiply parentheses

G*2G-4.2G-1=0

Wy multiply elements

2G^2-4.2G-1=0

a = 2; b = -4.2; c = -1;
Δ = b2-4ac
Δ = -4.22-4·2·(-1)
Δ = 25.64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4.2)-\sqrt{25.64}}{2*2}=\frac{4.2-\sqrt{25.64}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.2)+\sqrt{25.64}}{2*2}=\frac{4.2+\sqrt{25.64}}{4}
$