G(-6)=x+3/x-1

Solution for G(-6)=x+3/x-1 equation:

(-6)=G+3/G-1

We move all terms to the left:

(-6)-(G+3/G-1)=0


Domain of the equation: G-1)!=0

G∈R


We add all the numbers together, and all the variables

-(G+3/G-1)-6=0

We get rid of parentheses

-G-3/G+1-6=0

We multiply all the terms by the denominator


-G*G+1*G-6*G-3=0

We add all the numbers together, and all the variables

-5G-G*G-3=0

Wy multiply elements

-1G^2-5G-3=0

a = -1; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·(-1)·(-3)
Δ = 13
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{-(-5)-\sqrt{13}}{2*-1}=\frac{5-\sqrt{13}}{-2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*-1}=\frac{5+\sqrt{13}}{-2}
$