3x-2/4x+2=6

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

3x-2/4x+2=6

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

3x-2/4x-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-16x-2=0

a = 12; b = -16; c = -2;
Δ = b2-4ac
Δ = -162-4·12·(-2)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{22}}{2*12}=\frac{16-4\sqrt{22}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{22}}{2*12}=\frac{16+4\sqrt{22}}{24}
$