12x-8/4x=2

Solution for 12x-8/4x=2 equation:

12x-8/4x=2

We move all terms to the left:

12x-8/4x-(2)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


12x*4x-2*4x-8=0

Wy multiply elements

48x^2-8x-8=0

a = 48; b = -8; c = -8;
Δ = b2-4ac
Δ = -82-4·48·(-8)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-40}{2*48}=\frac{-32}{96}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+40}{2*48}=\frac{48}{96}
=1/2
$