6+2/3x=11-x

Solution for 6+2/3x=11-x equation:

6+2/3x=11-x

We move all terms to the left:

6+2/3x-(11-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

2/3x-(-1x+11)+6=0

We get rid of parentheses

2/3x+1x-11+6=0

We multiply all the terms by the denominator


1x*3x-11*3x+6*3x+2=0

Wy multiply elements

3x^2-33x+18x+2=0

We add all the numbers together, and all the variables

3x^2-15x+2=0

a = 3; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·3·2
Δ = 201
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{201}}{2*3}=\frac{15-\sqrt{201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{201}}{2*3}=\frac{15+\sqrt{201}}{6}
$