360/x=x

Solution for 360/x=x equation:

360/x=x

We move all terms to the left:

360/x-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+360/x=0

We multiply all the terms by the denominator


-1x*x+360=0

Wy multiply elements

-1x^2+360=0

a = -1; b = 0; c = +360;
Δ = b2-4ac
Δ = 02-4·(-1)·360
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-1}=\frac{0-12\sqrt{10}}{-2}
=-\frac{12\sqrt{10}}{-2}
=-\frac{6\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-1}=\frac{0+12\sqrt{10}}{-2}
=\frac{12\sqrt{10}}{-2}
=\frac{6\sqrt{10}}{-1}
$