(2*x)=(2+1)-8/(9*x)

Solution for (2*x)=(2+1)-8/(9*x) equation:

(2x)=(2+1)-8/(9x)

We move all terms to the left:

(2x)-((2+1)-8/(9x))=0


Domain of the equation: 9x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(3-8/9x)=0

We get rid of parentheses

2x+8/9x-3=0

We multiply all the terms by the denominator


2x*9x-3*9x+8=0

Wy multiply elements

18x^2-27x+8=0

a = 18; b = -27; c = +8;
Δ = b2-4ac
Δ = -272-4·18·8
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{17}}{2*18}=\frac{27-3\sqrt{17}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{17}}{2*18}=\frac{27+3\sqrt{17}}{36}
$