12/3x+14/x=2

Solution for 12/3x+14/x=2 equation:

12/3x+14/x=2

We move all terms to the left:

12/3x+14/x-(2)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We calculate fractions


12x/3x^2+42x/3x^2-2=0

We multiply all the terms by the denominator


12x+42x-2*3x^2=0

We add all the numbers together, and all the variables

54x-2*3x^2=0

Wy multiply elements

-6x^2+54x=0

a = -6; b = 54; c = 0;
Δ = b2-4ac
Δ = 542-4·(-6)·0
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-54}{2*-6}=\frac{-108}{-12}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+54}{2*-6}=\frac{0}{-12}
=0
$