2x+3=2/3x-1

Solution for 2x+3=2/3x-1 equation:

2x+3=2/3x-1

We move all terms to the left:

2x+3-(2/3x-1)=0


Domain of the equation: 3x-1)!=0

x∈R


We get rid of parentheses

2x-2/3x+1+3=0

We multiply all the terms by the denominator


2x*3x+1*3x+3*3x-2=0

Wy multiply elements

6x^2+3x+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 = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*6}=\frac{-12-8\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*6}=\frac{-12+8\sqrt{3}}{12}
$