x/3x-6=2x-9=

Solution for x/3x-6=2x-9= equation:

x/3x-6=2x-9=

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

x/3x-2x+9-6=0

We multiply all the terms by the denominator


x-2x*3x+9*3x-6*3x=0

Wy multiply elements

-6x^2+x+27x-18x=0

We add all the numbers together, and all the variables

-6x^2+10x=0

a = -6; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-6)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-6}=\frac{0}{-12}
=0
$