3x-2/x=6+4x

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

3x-2/x=6+4x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

3x^2-4x^2-6x-2=0

We add all the numbers together, and all the variables

-1x^2-6x-2=0

a = -1; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·(-1)·(-2)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{7}}{2*-1}=\frac{6-2\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{7}}{2*-1}=\frac{6+2\sqrt{7}}{-2}
$