-x-1=1/3x+3

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

-x-1=1/3x+3

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-3x^2-9x-3x-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 = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*-3}=\frac{12-2\sqrt{33}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*-3}=\frac{12+2\sqrt{33}}{-6}
$