6+2/3x=x-3

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

6+2/3x=x-3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2+9x+18x+2=0

We add all the numbers together, and all the variables

-3x^2+27x+2=0

a = -3; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·(-3)·2
Δ = 753
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-\sqrt{753}}{2*-3}=\frac{-27-\sqrt{753}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{753}}{2*-3}=\frac{-27+\sqrt{753}}{-6}
$