-3/x=-1/3x-3

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

-3/x=-1/3x-3

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

9x^2+x+(-9x)=0

We get rid of parentheses

9x^2+x-9x=0

We add all the numbers together, and all the variables

9x^2-8x=0

a = 9; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·9·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*9}=\frac{16}{18}
=8/9
$