2x+23=2/9x

Solution for 2x+23=2/9x equation:

2x+23=2/9x

We move all terms to the left:

2x+23-(2/9x)=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-(+2/9x)+23=0

We get rid of parentheses

2x-2/9x+23=0

We multiply all the terms by the denominator


2x*9x+23*9x-2=0

Wy multiply elements

18x^2+207x-2=0

a = 18; b = 207; c = -2;
Δ = b2-4ac
Δ = 2072-4·18·(-2)
Δ = 42993
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:

$\sqrt{\Delta}=\sqrt{42993}=\sqrt{9*4777}=\sqrt{9}*\sqrt{4777}=3\sqrt{4777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(207)-3\sqrt{4777}}{2*18}=\frac{-207-3\sqrt{4777}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(207)+3\sqrt{4777}}{2*18}=\frac{-207+3\sqrt{4777}}{36}
$