x+3=2/3x+2

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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} $

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