6+9x=11/3x

Solution for 6+9x=11/3x equation:

6+9x=11/3x

We move all terms to the left:

6+9x-(11/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+11/3x)+6=0

We get rid of parentheses

9x-11/3x+6=0

We multiply all the terms by the denominator


9x*3x+6*3x-11=0

Wy multiply elements

27x^2+18x-11=0

a = 27; b = 18; c = -11;
Δ = b2-4ac
Δ = 182-4·27·(-11)
Δ = 1512
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:

$\sqrt{\Delta}=\sqrt{1512}=\sqrt{36*42}=\sqrt{36}*\sqrt{42}=6\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{42}}{2*27}=\frac{-18-6\sqrt{42}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{42}}{2*27}=\frac{-18+6\sqrt{42}}{54}
$