5x=1/3(6x)

Solution for 5x=1/3(6x) equation:

5x=1/3(6x)

We move all terms to the left:

5x-(1/3(6x))=0


Domain of the equation: 36x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x-(+1/36x)=0

We get rid of parentheses

5x-1/36x=0

We multiply all the terms by the denominator


5x*36x-1=0

Wy multiply elements

180x^2-1=0

a = 180; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·180·(-1)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*180}=\frac{0-12\sqrt{5}}{360}
=-\frac{12\sqrt{5}}{360}
=-\frac{\sqrt{5}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*180}=\frac{0+12\sqrt{5}}{360}
=\frac{12\sqrt{5}}{360}
=\frac{\sqrt{5}}{30}
$