3x+11=1/3x

Solution for 3x+11=1/3x equation:

3x+11=1/3x

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-1/3x+11=0

We multiply all the terms by the denominator


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

Wy multiply elements

9x^2+33x-1=0

a = 9; b = 33; c = -1;
Δ = b2-4ac
Δ = 332-4·9·(-1)
Δ = 1125
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-15\sqrt{5}}{2*9}=\frac{-33-15\sqrt{5}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+15\sqrt{5}}{2*9}=\frac{-33+15\sqrt{5}}{18}
$