12x-4/x=2

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

12x-4/x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

12x^2-2x-4=0

a = 12; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·12·(-4)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*12}=\frac{-12}{24}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*12}=\frac{16}{24}
=2/3
$