9(2x+1)=81x-2/3x

Solution for 9(2x+1)=81x-2/3x equation:

9(2x+1)=81x-2/3x

We move all terms to the left:

9(2x+1)-(81x-2/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9(2x+1)-(+81x-2/3x)=0

We multiply parentheses

18x-(+81x-2/3x)+9=0

We get rid of parentheses

18x-81x+2/3x+9=0

We multiply all the terms by the denominator


18x*3x-81x*3x+9*3x+2=0

Wy multiply elements

54x^2-243x^2+27x+2=0

We add all the numbers together, and all the variables

-189x^2+27x+2=0

a = -189; b = 27; c = +2;
Δ = b2-4ac
Δ = 272-4·(-189)·2
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{249}}{2*-189}=\frac{-27-3\sqrt{249}}{-378}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{249}}{2*-189}=\frac{-27+3\sqrt{249}}{-378}
$