6x-3/3=12/2x

Solution for 6x-3/3=12/2x equation:

6x-3/3=12/2x

We move all terms to the left:

6x-3/3-(12/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

6x-12/2x-1=0

We multiply all the terms by the denominator


6x*2x-1*2x-12=0

Wy multiply elements

12x^2-2x-12=0

a = 12; b = -2; c = -12;
Δ = b2-4ac
Δ = -22-4·12·(-12)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{145}}{2*12}=\frac{2-2\sqrt{145}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{145}}{2*12}=\frac{2+2\sqrt{145}}{24}
$