x/6x-4=2x+6

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

x/6x-4=2x+6

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We get rid of parentheses

x/6x-2x-6-4=0

We multiply all the terms by the denominator


x-2x*6x-6*6x-4*6x=0

Wy multiply elements

-12x^2+x-36x-24x=0

We add all the numbers together, and all the variables

-12x^2-59x=0

a = -12; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·(-12)·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*-12}=\frac{118}{-24}
=-4+11/12
$