x=3642/3x

Solution for x=3642/3x equation:

x=3642/3x

We move all terms to the left:

x-(3642/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+3642/3x)=0

We get rid of parentheses

x-3642/3x=0

We multiply all the terms by the denominator


x*3x-3642=0

Wy multiply elements

3x^2-3642=0

a = 3; b = 0; c = -3642;
Δ = b2-4ac
Δ = 02-4·3·(-3642)
Δ = 43704
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:

$\sqrt{\Delta}=\sqrt{43704}=\sqrt{36*1214}=\sqrt{36}*\sqrt{1214}=6\sqrt{1214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{1214}}{2*3}=\frac{0-6\sqrt{1214}}{6}
=-\frac{6\sqrt{1214}}{6}
=-\sqrt{1214}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{1214}}{2*3}=\frac{0+6\sqrt{1214}}{6}
=\frac{6\sqrt{1214}}{6}
=\sqrt{1214}
$