4/x+12-2/x-12=5x/x+12,x-12

Solution for 4/x+12-2/x-12=5x/x+12,x-12 equation:

4/x+12-2/x-12=5x/x+12.x-12

We move all terms to the left:

4/x+12-2/x-12-(5x/x+12.x-12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: x+12.x-12)!=0

x∈R


We add all the numbers together, and all the variables

4/x-2/x-(12.x+5x/x-12)+12-12=0

We add all the numbers together, and all the variables

4/x-2/x-(12.x+5x/x-12)=0

We get rid of parentheses

4/x-2/x-12.x-5x/x+12=0

We multiply all the terms by the denominator


-(12.x)*x-5x+12*x+4-2=0

We add all the numbers together, and all the variables

-(+12.x)*x-5x+12*x+4-2=0

We add all the numbers together, and all the variables

7x-(+12.x)*x+2=0

We multiply parentheses

-12x^2+7x+2=0

a = -12; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-12)·2
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{145}}{2*-12}=\frac{-7-\sqrt{145}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*-12}=\frac{-7+\sqrt{145}}{-24}
$