2/x-4+1=3/3x-12

Solution for 2/x-4+1=3/3x-12 equation:

2/x-4+1=3/3x-12

We move all terms to the left:

2/x-4+1-(3/3x-12)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-12)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


6x/3x^2+(-3x)/3x^2+12-3=0

We add all the numbers together, and all the variables

6x/3x^2+(-3x)/3x^2+9=0

We multiply all the terms by the denominator


6x+(-3x)+9*3x^2=0

Wy multiply elements

27x^2+6x+(-3x)=0

We get rid of parentheses

27x^2+6x-3x=0

We add all the numbers together, and all the variables

27x^2+3x=0

a = 27; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·27·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*27}=\frac{-6}{54}
=-1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*27}=\frac{0}{54}
=0
$