2/3x+6=3/6x-5

Solution for 2/3x+6=3/6x-5 equation:

2/3x+6=3/6x-5

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-5)!=0

x∈R


We get rid of parentheses

2/3x-3/6x+5+6=0

We calculate fractions


12x/18x^2+(-9x)/18x^2+5+6=0

We add all the numbers together, and all the variables

12x/18x^2+(-9x)/18x^2+11=0

We multiply all the terms by the denominator


12x+(-9x)+11*18x^2=0

Wy multiply elements

198x^2+12x+(-9x)=0

We get rid of parentheses

198x^2+12x-9x=0

We add all the numbers together, and all the variables

198x^2+3x=0

a = 198; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·198·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*198}=\frac{-6}{396}
=-1/66
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*198}=\frac{0}{396}
=0
$