-3/x+3=6/3x-2

Solution for -3/x+3=6/3x-2 equation:

-3/x+3=6/3x-2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x-2)!=0

x∈R


We get rid of parentheses

-3/x-6/3x+2+3=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-9x)/3x^2+(-6x)/3x^2+5=0

We multiply all the terms by the denominator


(-9x)+(-6x)+5*3x^2=0

Wy multiply elements

15x^2+(-9x)+(-6x)=0

We get rid of parentheses

15x^2-9x-6x=0

We add all the numbers together, and all the variables

15x^2-15x=0

a = 15; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·15·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*15}=\frac{0}{30}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*15}=\frac{30}{30}
=1
$