162/3^2x-4=2

Solution for 162/3^2x-4=2 equation:

162/3^2x-4=2

We move all terms to the left:

162/3^2x-4-(2)=0


Domain of the equation: 3^2x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

162/3^2x-6=0

We multiply all the terms by the denominator


-6*3^2x+162=0

Wy multiply elements

-18x^2+162=0

a = -18; b = 0; c = +162;
Δ = b2-4ac
Δ = 02-4·(-18)·162
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108}{2*-18}=\frac{-108}{-36}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108}{2*-18}=\frac{108}{-36}
=-3
$