6x-8/2x=4

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

6x-8/2x=4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-8x-8=0

a = 12; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·12·(-8)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{7}}{2*12}=\frac{8-8\sqrt{7}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{7}}{2*12}=\frac{8+8\sqrt{7}}{24}
$