G(x)=4/x-6+5

Solution for G(x)=4/x-6+5 equation:

(G)=4/G-6+5

We move all terms to the left:

(G)-(4/G-6+5)=0


Domain of the equation: G-6+5)!=0

We move all terms containing G to the left, all other terms to the right

G+5)!=6

G∈R


We add all the numbers together, and all the variables

G-(4/G-1)=0

We get rid of parentheses

G-4/G+1=0

We multiply all the terms by the denominator


G*G+1*G-4=0

We add all the numbers together, and all the variables

G+G*G-4=0

Wy multiply elements

G^2+G-4=0

a = 1; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·1·(-4)
Δ = 17
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{-(1)-\sqrt{17}}{2*1}=\frac{-1-\sqrt{17}}{2}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{17}}{2*1}=\frac{-1+\sqrt{17}}{2}
$