12/3x+6/1=4x+2

Solution for 12/3x+6/1=4x+2 equation:

12/3x+6/1=4x+2

We move all terms to the left:

12/3x+6/1-(4x+2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

12/3x-(4x+2)=0

We get rid of parentheses

12/3x-4x-2=0

We multiply all the terms by the denominator


-4x*3x-2*3x+12=0

Wy multiply elements

-12x^2-6x+12=0

a = -12; b = -6; c = +12;
Δ = b2-4ac
Δ = -62-4·(-12)·12
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{17}}{2*-12}=\frac{6-6\sqrt{17}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{17}}{2*-12}=\frac{6+6\sqrt{17}}{-24}
$