4/x-1/6x=2

Solution for 4/x-1/6x=2 equation:

4/x-1/6x=2

We move all terms to the left:

4/x-1/6x-(2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


24x/6x^2+(-x)/6x^2-2=0

We add all the numbers together, and all the variables

24x/6x^2+(-1x)/6x^2-2=0

We multiply all the terms by the denominator


24x+(-1x)-2*6x^2=0

Wy multiply elements

-12x^2+24x+(-1x)=0

We get rid of parentheses

-12x^2+24x-1x=0

We add all the numbers together, and all the variables

-12x^2+23x=0

a = -12; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-12}=\frac{-46}{-24}
=1+11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-12}=\frac{0}{-24}
=0
$