-2/3x+2=x+6

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

-2/3x+2=x+6

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-18x+6x-2=0

We add all the numbers together, and all the variables

-3x^2-12x-2=0

a = -3; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·(-3)·(-2)
Δ = 120
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-3}=\frac{12-2\sqrt{30}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-3}=\frac{12+2\sqrt{30}}{-6}
$