x/6x-2x=24

Solution for x/6x-2x=24 equation:

x/6x-2x=24

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-2x+x/6x-24=0

We multiply all the terms by the denominator


-2x*6x+x-24*6x=0

We add all the numbers together, and all the variables

x-2x*6x-24*6x=0

Wy multiply elements

-12x^2+x-144x=0

We add all the numbers together, and all the variables

-12x^2-143x=0

a = -12; b = -143; c = 0;
Δ = b2-4ac
Δ = -1432-4·(-12)·0
Δ = 20449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20449}=143$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-143)-143}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-143)+143}{2*-12}=\frac{286}{-24}
=-11+11/12
$