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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


6x*3x)3x)-((-3*3x)3x)+2=0

Wy multiply elements

18x^2-9x=0

a = 18; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·18·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*18}=\frac{0}{36}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*18}=\frac{18}{36}
=1/2
$