G(n)=1/2n-4

Solution for G(n)=1/2n-4 equation:

(G)=1/2G-4

We move all terms to the left:

(G)-(1/2G-4)=0


Domain of the equation: 2G-4)!=0

G∈R


We get rid of parentheses

G-1/2G+4=0

We multiply all the terms by the denominator


G*2G+4*2G-1=0

Wy multiply elements

2G^2+8G-1=0

a = 2; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·2·(-1)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{2}}{2*2}=\frac{-8-6\sqrt{2}}{4}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{2}}{2*2}=\frac{-8+6\sqrt{2}}{4}
$