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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

6x-8/2x-4-2=0

We add all the numbers together, and all the variables

6x-8/2x-6=0

We multiply all the terms by the denominator


6x*2x-6*2x-8=0

Wy multiply elements

12x^2-12x-8=0

a = 12; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·12·(-8)
Δ = 528
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:

$\sqrt{\Delta}=\sqrt{528}=\sqrt{16*33}=\sqrt{16}*\sqrt{33}=4\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{33}}{2*12}=\frac{12-4\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{33}}{2*12}=\frac{12+4\sqrt{33}}{24}
$