1/3x-2=x+3

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

1/3x-2=x+3

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-9x-6x+1=0

We add all the numbers together, and all the variables

-3x^2-15x+1=0

a = -3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·(-3)·1
Δ = 237
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{237}}{2*-3}=\frac{15-\sqrt{237}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{237}}{2*-3}=\frac{15+\sqrt{237}}{-6}
$