2x+3=7-2/3x

Solution for 2x+3=7-2/3x equation:

2x+3=7-2/3x

We move all terms to the left:

2x+3-(7-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(-2/3x+7)+3=0

We get rid of parentheses

2x+2/3x-7+3=0

We multiply all the terms by the denominator


2x*3x-7*3x+3*3x+2=0

Wy multiply elements

6x^2-21x+9x+2=0

We add all the numbers together, and all the variables

6x^2-12x+2=0

a = 6; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·6·2
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{6}}{2*6}=\frac{12-4\sqrt{6}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{6}}{2*6}=\frac{12+4\sqrt{6}}{12}
$