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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

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}
$