3x+6/2x-12=0

Solution for 3x+6/2x-12=0 equation:

3x+6/2x-12=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-12*2x+6=0

Wy multiply elements

6x^2-24x+6=0

a = 6; b = -24; c = +6;
Δ = b2-4ac
Δ = -242-4·6·6
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{3}}{2*6}=\frac{24-12\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{3}}{2*6}=\frac{24+12\sqrt{3}}{12}
$