3x=1/2(6x)

Solution for 3x=1/2(6x) equation:

3x=1/2(6x)

We move all terms to the left:

3x-(1/2(6x))=0


Domain of the equation: 26x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+1/26x)=0

We get rid of parentheses

3x-1/26x=0

We multiply all the terms by the denominator


3x*26x-1=0

Wy multiply elements

78x^2-1=0

a = 78; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·78·(-1)
Δ = 312
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:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{78}}{2*78}=\frac{0-2\sqrt{78}}{156}
=-\frac{2\sqrt{78}}{156}
=-\frac{\sqrt{78}}{78}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{78}}{2*78}=\frac{0+2\sqrt{78}}{156}
=\frac{2\sqrt{78}}{156}
=\frac{\sqrt{78}}{78}
$