2x+6/2x-6=4

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

2x+6/2x-6=4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+6/2x-10=0

We multiply all the terms by the denominator


2x*2x-10*2x+6=0

Wy multiply elements

4x^2-20x+6=0

a = 4; b = -20; c = +6;
Δ = b2-4ac
Δ = -202-4·4·6
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{-(-20)-4\sqrt{19}}{2*4}=\frac{20-4\sqrt{19}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{19}}{2*4}=\frac{20+4\sqrt{19}}{8}
$