12x/x+1+24/2x=28/x

Solution for 12x/x+1+24/2x=28/x equation:

12x/x+1+24/2x=28/x

We move all terms to the left:

12x/x+1+24/2x-(28/x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

12x/x+24/2x-(+28/x)+1=0

We get rid of parentheses

12x/x+24/2x-28/x+1=0

We calculate fractions


(-44x)/2x^2+24x/2x^2+1=0

We multiply all the terms by the denominator


(-44x)+24x+1*2x^2=0

We add all the numbers together, and all the variables

24x+(-44x)+1*2x^2=0

Wy multiply elements

2x^2+24x+(-44x)=0

We get rid of parentheses

2x^2+24x-44x=0

We add all the numbers together, and all the variables

2x^2-20x=0

a = 2; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·2·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*2}=\frac{40}{4}
=10
$