3x-12/2x=2

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

3x-12/2x=2

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-4x-12=0

a = 6; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·6·(-12)
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{19}}{2*6}=\frac{4-4\sqrt{19}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{19}}{2*6}=\frac{4+4\sqrt{19}}{12}
$