105/x=x

Solution for 105/x=x equation:

105/x=x

We move all terms to the left:

105/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+105/x=0

We multiply all the terms by the denominator


-1x*x+105=0

Wy multiply elements

-1x^2+105=0

a = -1; b = 0; c = +105;
Δ = b2-4ac
Δ = 02-4·(-1)·105
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*-1}=\frac{0-2\sqrt{105}}{-2}
=-\frac{2\sqrt{105}}{-2}
=-\frac{\sqrt{105}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-1}=\frac{0+2\sqrt{105}}{-2}
=\frac{2\sqrt{105}}{-2}
=\frac{\sqrt{105}}{-1}
$