2x-5=-1/3x+2

Solution for 2x-5=-1/3x+2 equation:

2x-5=-1/3x+2

We move all terms to the left:

2x-5-(-1/3x+2)=0


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

x∈R


We get rid of parentheses

2x+1/3x-2-5=0

We multiply all the terms by the denominator


2x*3x-2*3x-5*3x+1=0

Wy multiply elements

6x^2-6x-15x+1=0

We add all the numbers together, and all the variables

6x^2-21x+1=0

a = 6; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·6·1
Δ = 417
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{-(-21)-\sqrt{417}}{2*6}=\frac{21-\sqrt{417}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{417}}{2*6}=\frac{21+\sqrt{417}}{12}
$