/3x+11=3x-11

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

/3x+11=3x-11

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-9x^2+33x+33x=0

We add all the numbers together, and all the variables

-9x^2+66x=0

a = -9; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·(-9)·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*-9}=\frac{-132}{-18}
=7+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*-9}=\frac{0}{-18}
=0
$