6-11/3x=-1-x

Solution for 6-11/3x=-1-x equation:

6-11/3x=-1-x

We move all terms to the left:

6-11/3x-(-1-x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-11/3x-(-1x-1)+6=0

We get rid of parentheses

-11/3x+1x+1+6=0

We multiply all the terms by the denominator


1x*3x+1*3x+6*3x-11=0

Wy multiply elements

3x^2+3x+18x-11=0

We add all the numbers together, and all the variables

3x^2+21x-11=0

a = 3; b = 21; c = -11;
Δ = b2-4ac
Δ = 212-4·3·(-11)
Δ = 573
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{573}}{2*3}=\frac{-21-\sqrt{573}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{573}}{2*3}=\frac{-21+\sqrt{573}}{6}
$