(x)(1/3(x))=162

Solution for (x)(1/3(x))=162 equation:

(x)(1/3(x))=162

We move all terms to the left:

(x)(1/3(x))-(162)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+1/3x)-162=0

We multiply parentheses

x^2-162=0

a = 1; b = 0; c = -162;
Δ = b2-4ac
Δ = 02-4·1·(-162)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{2}}{2*1}=\frac{0-18\sqrt{2}}{2}
=-\frac{18\sqrt{2}}{2}
=-9\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{2}}{2*1}=\frac{0+18\sqrt{2}}{2}
=\frac{18\sqrt{2}}{2}
=9\sqrt{2}
$