-1/3x=3/6x-9

Solution for -1/3x=3/6x-9 equation:

-1/3x=3/6x-9

We move all terms to the left:

-1/3x-(3/6x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-9)!=0

x∈R


We get rid of parentheses

-1/3x-3/6x+9=0

We calculate fractions


(-6x)/18x^2+(-9x)/18x^2+9=0

We multiply all the terms by the denominator


(-6x)+(-9x)+9*18x^2=0

Wy multiply elements

162x^2+(-6x)+(-9x)=0

We get rid of parentheses

162x^2-6x-9x=0

We add all the numbers together, and all the variables

162x^2-15x=0

a = 162; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·162·0
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*162}=\frac{0}{324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*162}=\frac{30}{324}
=5/54
$