G(x)=-1/3x+4

Solution for G(x)=-1/3x+4 equation:

(G)=-1/3G+4

We move all terms to the left:

(G)-(-1/3G+4)=0


Domain of the equation: 3G+4)!=0

G∈R


We get rid of parentheses

G+1/3G-4=0

We multiply all the terms by the denominator


G*3G-4*3G+1=0

Wy multiply elements

3G^2-12G+1=0

a = 3; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·3·1
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*3}=\frac{12-2\sqrt{33}}{6}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*3}=\frac{12+2\sqrt{33}}{6}
$