2x=360/x

Solution for 2x=360/x equation:

2x=360/x

We move all terms to the left:

2x-(360/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+360/x)=0

We get rid of parentheses

2x-360/x=0

We multiply all the terms by the denominator


2x*x-360=0

Wy multiply elements

2x^2-360=0

a = 2; b = 0; c = -360;
Δ = b2-4ac
Δ = 02-4·2·(-360)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*2}=\frac{0-24\sqrt{5}}{4}
=-\frac{24\sqrt{5}}{4}
=-6\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*2}=\frac{0+24\sqrt{5}}{4}
=\frac{24\sqrt{5}}{4}
=6\sqrt{5}
$