x/6x-4=-4+6x

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

x/6x-4=-4+6x

We move all terms to the left:

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


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x/6x-6x+4-4=0

We multiply all the terms by the denominator


x-6x*6x+4*6x-4*6x=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-36x^2+x=0

a = -36; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-36)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-36}=\frac{-2}{-72}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-36}=\frac{0}{-72}
=0
$