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

Solution for 12x/(3x^2-12)+2=0 equation:

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


Domain of the equation: (3x^2-12)!=0

We move all terms containing x to the left, all other terms to the right

3x^2!=12

x^2!=12/3

x^2!=√4

x!=2

x∈R


We multiply all the terms by the denominator


12x+2*(3x^2-12)=0

We multiply parentheses

6x^2+12x-24=0

a = 6; b = 12; c = -24;
Δ = b2-4ac
Δ = 122-4·6·(-24)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{5}}{2*6}=\frac{-12-12\sqrt{5}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{5}}{2*6}=\frac{-12+12\sqrt{5}}{12}
$