3x=3/5x

Solution for 3x=3/5x equation:

3x=3/5x

We move all terms to the left:

3x-(3/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+3/5x)=0

We get rid of parentheses

3x-3/5x=0

We multiply all the terms by the denominator


3x*5x-3=0

Wy multiply elements

15x^2-3=0

a = 15; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·15·(-3)
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{5}}{2*15}=\frac{0-6\sqrt{5}}{30}
=-\frac{6\sqrt{5}}{30}
=-\frac{\sqrt{5}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{5}}{2*15}=\frac{0+6\sqrt{5}}{30}
=\frac{6\sqrt{5}}{30}
=\frac{\sqrt{5}}{5}
$