G(x)=3/5x

Solution for G(x)=3/5x equation:

(G)=3/5G

We move all terms to the left:

(G)-(3/5G)=0


Domain of the equation: 5G)!=0

G!=0/1

G!=0

G∈R


We add all the numbers together, and all the variables

G-(+3/5G)=0

We get rid of parentheses

G-3/5G=0

We multiply all the terms by the denominator


G*5G-3=0

Wy multiply elements

5G^2-3=0

a = 5; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·5·(-3)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$G_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*5}=\frac{0-2\sqrt{15}}{10}
=-\frac{2\sqrt{15}}{10}
=-\frac{\sqrt{15}}{5}
$
$G_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*5}=\frac{0+2\sqrt{15}}{10}
=\frac{2\sqrt{15}}{10}
=\frac{\sqrt{15}}{5}
$