2x-3=1/3x+2

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

2x-3=1/3x+2

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-6x-9x-1=0

We add all the numbers together, and all the variables

6x^2-15x-1=0

a = 6; b = -15; c = -1;
Δ = b2-4ac
Δ = -152-4·6·(-1)
Δ = 249
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{-(-15)-\sqrt{249}}{2*6}=\frac{15-\sqrt{249}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{249}}{2*6}=\frac{15+\sqrt{249}}{12}
$