x/2x-4=x+3/12

Solution for x/2x-4=x+3/12 equation:

x/2x-4=x+3/12

We move all terms to the left:

x/2x-4-(x+3/12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x/2x-(+x+3/12)-4=0

We get rid of parentheses

x/2x-x-4-3/12=0

We calculate fractions


-x+12x/24x+(-6x)/24x-4=0

We add all the numbers together, and all the variables

-1x+12x/24x+(-6x)/24x-4=0

We multiply all the terms by the denominator


-1x*24x+12x+(-6x)-4*24x=0

We add all the numbers together, and all the variables

12x-1x*24x+(-6x)-4*24x=0

Wy multiply elements

-24x^2+12x+(-6x)-96x=0

We get rid of parentheses

-24x^2+12x-6x-96x=0

We add all the numbers together, and all the variables

-24x^2-90x=0

a = -24; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·(-24)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*-24}=\frac{0}{-48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*-24}=\frac{180}{-48}
=-3+3/4
$