243/x=x

Solution for 243/x=x equation:

243/x=x

We move all terms to the left:

243/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+243/x=0

We multiply all the terms by the denominator


-1x*x+243=0

Wy multiply elements

-1x^2+243=0

a = -1; b = 0; c = +243;
Δ = b2-4ac
Δ = 02-4·(-1)·243
Δ = 972
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:

$\sqrt{\Delta}=\sqrt{972}=\sqrt{324*3}=\sqrt{324}*\sqrt{3}=18\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{3}}{2*-1}=\frac{0-18\sqrt{3}}{-2}
=-\frac{18\sqrt{3}}{-2}
=-\frac{9\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{3}}{2*-1}=\frac{0+18\sqrt{3}}{-2}
=\frac{18\sqrt{3}}{-2}
=\frac{9\sqrt{3}}{-1}
$