G(x)=5+6/x

Solution for G(x)=5+6/x equation:

(G)=5+6/G

We move all terms to the left:

(G)-(5+6/G)=0


Domain of the equation: G)!=0

G!=0/1

G!=0

G∈R


We add all the numbers together, and all the variables

G-(6/G+5)=0

We get rid of parentheses

G-6/G-5=0

We multiply all the terms by the denominator


G*G-5*G-6=0

We add all the numbers together, and all the variables

-5G+G*G-6=0

Wy multiply elements

G^2-5G-6=0

a = 1; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·1·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-7}{2*1}=\frac{-2}{2}
=-1
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+7}{2*1}=\frac{12}{2}
=6
$