243/x=3x

Solution for 243/x=3x equation:

243/x=3x

We move all terms to the left:

243/x-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+243/x=0

We multiply all the terms by the denominator


-3x*x+243=0

Wy multiply elements

-3x^2+243=0

a = -3; b = 0; c = +243;
Δ = b2-4ac
Δ = 02-4·(-3)·243
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*-3}=\frac{-54}{-6}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*-3}=\frac{54}{-6}
=-9
$