12/x+1=1/3x+2

Solution for 12/x+1=1/3x+2 equation:

12/x+1=1/3x+2

We move all terms to the left:

12/x+1-(1/3x+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

12/x-1/3x-2+1=0

We calculate fractions


36x/3x^2+(-x)/3x^2-2+1=0

We add all the numbers together, and all the variables

36x/3x^2+(-1x)/3x^2-2+1=0

We add all the numbers together, and all the variables

36x/3x^2+(-1x)/3x^2-1=0

We multiply all the terms by the denominator


36x+(-1x)-1*3x^2=0

Wy multiply elements

-3x^2+36x+(-1x)=0

We get rid of parentheses

-3x^2+36x-1x=0

We add all the numbers together, and all the variables

-3x^2+35x=0

a = -3; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-3)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-3}=\frac{-70}{-6}
=11+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-3}=\frac{0}{-6}
=0
$