G(x)=1/2x+2

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

(G)=1/2G+2

We move all terms to the left:

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


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

G∈R


We get rid of parentheses

G-1/2G-2=0

We multiply all the terms by the denominator


G*2G-2*2G-1=0

Wy multiply elements

2G^2-4G-1=0

a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4}
$