3x(1/6x+3)=2x

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

3x(1/6x+3)=2x

We move all terms to the left:

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


Domain of the equation: 6x+3)!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-2x+9x=0

We add all the numbers together, and all the variables

3x^2+7x=0

a = 3; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·3·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*3}=\frac{-14}{6}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*3}=\frac{0}{6}
=0
$