7/x=1/3x-6

Solution for 7/x=1/3x-6 equation:

7/x=1/3x-6

We move all terms to the left:

7/x-(1/3x-6)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-6)!=0

x∈R


We get rid of parentheses

7/x-1/3x+6=0

We calculate fractions


21x/3x^2+(-x)/3x^2+6=0

We add all the numbers together, and all the variables

21x/3x^2+(-1x)/3x^2+6=0

We multiply all the terms by the denominator


21x+(-1x)+6*3x^2=0

Wy multiply elements

18x^2+21x+(-1x)=0

We get rid of parentheses

18x^2+21x-1x=0

We add all the numbers together, and all the variables

18x^2+20x=0

a = 18; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·18·0
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*18}=\frac{-40}{36}
=-1+1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*18}=\frac{0}{36}
=0
$