1/3x-3=x+1

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

1/3x-3=x+1

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2-12x+1=0

a = -3; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-3)·1
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{39}}{2*-3}=\frac{12-2\sqrt{39}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{39}}{2*-3}=\frac{12+2\sqrt{39}}{-6}
$