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!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

50x-2*2x^2=0

Wy multiply elements

-4x^2+50x=0

a = -4; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·(-4)·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*-4}=\frac{-100}{-8}
=12+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*-4}=\frac{0}{-8}
=0
$