3x-11=(1/3x)-8

Solution for 3x-11=(1/3x)-8 equation:

3x-11=(1/3x)-8

We move all terms to the left:

3x-11-((1/3x)-8)=0


Domain of the equation: 3x)-8)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-((+1/3x)-8)-11=0

We multiply all the terms by the denominator


3x*3x)-8)-((-11*3x)-8)+1=0

Wy multiply elements

9x^2-33x=0

a = 9; b = -33; c = 0;
Δ = b2-4ac
Δ = -332-4·9·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-33}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+33}{2*9}=\frac{66}{18}
=3+2/3
$