G(x)=1/2x+6

Solution for G(x)=1/2x+6 equation:

(G)=1/2G+6

We move all terms to the left:

(G)-(1/2G+6)=0


Domain of the equation: 2G+6)!=0

G∈R


We get rid of parentheses

G-1/2G-6=0

We multiply all the terms by the denominator


G*2G-6*2G-1=0

Wy multiply elements

2G^2-12G-1=0

a = 2; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·2·(-1)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{38}}{2*2}=\frac{12-2\sqrt{38}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{38}}{2*2}=\frac{12+2\sqrt{38}}{4}
$