10/12x-4=2/2x+2

Solution for 10/12x-4=2/2x+2 equation:

10/12x-4=2/2x+2

We move all terms to the left:

10/12x-4-(2/2x+2)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 2x+2)!=0

x∈R


We get rid of parentheses

10/12x-2/2x-2-4=0

We calculate fractions


20x/24x^2+(-24x)/24x^2-2-4=0

We add all the numbers together, and all the variables

20x/24x^2+(-24x)/24x^2-6=0

We multiply all the terms by the denominator


20x+(-24x)-6*24x^2=0

Wy multiply elements

-144x^2+20x+(-24x)=0

We get rid of parentheses

-144x^2+20x-24x=0

We add all the numbers together, and all the variables

-144x^2-4x=0

a = -144; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-144)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-144}=\frac{8}{-288}
=-1/36
$