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+15x-11=0

a = 3; b = 15; c = -11;
Δ = b2-4ac
Δ = 152-4·3·(-11)
Δ = 357
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{357}}{2*3}=\frac{-15-\sqrt{357}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{357}}{2*3}=\frac{-15+\sqrt{357}}{6}
$