2x+6/4x-8=-2

Solution for 2x+6/4x-8=-2 equation:

2x+6/4x-8=-2

We move all terms to the left:

2x+6/4x-8-(-2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

2x+6/4x-6=0

We multiply all the terms by the denominator


2x*4x-6*4x+6=0

Wy multiply elements

8x^2-24x+6=0

a = 8; b = -24; c = +6;
Δ = b2-4ac
Δ = -242-4·8·6
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{6}}{2*8}=\frac{24-8\sqrt{6}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{6}}{2*8}=\frac{24+8\sqrt{6}}{16}
$