G(x)=1/3x

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



(G)=1/3G
We move all terms to the left:
(G)-(1/3G)=0
Domain of the equation: 3G)!=0
G!=0/1
G!=0
G∈R
We add all the numbers together, and all the variables
G-(+1/3G)=0
We get rid of parentheses
G-1/3G=0
We multiply all the terms by the denominator
G*3G-1=0
Wy multiply elements
3G^2-1=0
a = 3; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·3·(-1)
Δ = 12
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:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*3}=\frac{0-2\sqrt{3}}{6} =-\frac{2\sqrt{3}}{6} =-\frac{\sqrt{3}}{3} $
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*3}=\frac{0+2\sqrt{3}}{6} =\frac{2\sqrt{3}}{6} =\frac{\sqrt{3}}{3} $

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