(7/x-4)+2=3/3x-12

Solution for (7/x-4)+2=3/3x-12 equation:

(7/x-4)+2=3/3x-12

We move all terms to the left:

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


Domain of the equation: x-4)!=0

x∈R



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

x∈R


We get rid of parentheses

7/x-3/3x-4+12+2=0

We calculate fractions


21x/3x^2+(-3x)/3x^2-4+12+2=0

We add all the numbers together, and all the variables

21x/3x^2+(-3x)/3x^2+10=0

We multiply all the terms by the denominator


21x+(-3x)+10*3x^2=0

Wy multiply elements

30x^2+21x+(-3x)=0

We get rid of parentheses

30x^2+21x-3x=0

We add all the numbers together, and all the variables

30x^2+18x=0

a = 30; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·30·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*30}=\frac{-36}{60}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*30}=\frac{0}{60}
=0
$