(12/x-2)+(26/2x+1)=5

Solution for (12/x-2)+(26/2x+1)=5 equation:

(12/x-2)+(26/2x+1)=5

We move all terms to the left:

(12/x-2)+(26/2x+1)-(5)=0


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

x∈R



Domain of the equation: 2x+1)!=0

x∈R


We get rid of parentheses

12/x+26/2x-2+1-5=0

We calculate fractions


24x/2x^2+26x/2x^2-2+1-5=0

We add all the numbers together, and all the variables

24x/2x^2+26x/2x^2-6=0

We multiply all the terms by the denominator


24x+26x-6*2x^2=0

We add all the numbers together, and all the variables

50x-6*2x^2=0

Wy multiply elements

-12x^2+50x=0

a = -12; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-12)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-50}{2*-12}=\frac{-100}{-24}
=4+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-12}=\frac{0}{-24}
=0
$