x+3=2/3x+2

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

x+3=2/3x+2

We move all terms to the left:

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


Domain of the equation: 3x+2)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

3x^2+3x-2=0

a = 3; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·3·(-2)
Δ = 33
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{-(3)-\sqrt{33}}{2*3}=\frac{-3-\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{33}}{2*3}=\frac{-3+\sqrt{33}}{6}
$