4/3x+2=6x

Solution for 4/3x+2=6x equation:

4/3x+2=6x

We move all terms to the left:

4/3x+2-(6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+4/3x+2=0

We multiply all the terms by the denominator


-6x*3x+2*3x+4=0

Wy multiply elements

-18x^2+6x+4=0

a = -18; b = 6; c = +4;
Δ = b2-4ac
Δ = 62-4·(-18)·4
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*-18}=\frac{-24}{-36}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*-18}=\frac{12}{-36}
=-1/3
$