9/x=-6/3x-3

Solution for 9/x=-6/3x-3 equation:

9/x=-6/3x-3

We move all terms to the left:

9/x-(-6/3x-3)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

9/x+6/3x+3=0

We calculate fractions


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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

33x+3*3x^2=0

Wy multiply elements

9x^2+33x=0

a = 9; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·9·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*9}=\frac{-66}{18}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*9}=\frac{0}{18}
=0
$