180(x-2)=360/x

Solution for 180(x-2)=360/x equation:

180(x-2)=360/x

We move all terms to the left:

180(x-2)-(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

180(x-2)-(+360/x)=0

We multiply parentheses

180x-(+360/x)-360=0

We get rid of parentheses

180x-360/x-360=0

We multiply all the terms by the denominator


180x*x-360*x-360=0

We add all the numbers together, and all the variables

-360x+180x*x-360=0

Wy multiply elements

180x^2-360x-360=0

a = 180; b = -360; c = -360;
Δ = b2-4ac
Δ = -3602-4·180·(-360)
Δ = 388800
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:

$\sqrt{\Delta}=\sqrt{388800}=\sqrt{129600*3}=\sqrt{129600}*\sqrt{3}=360\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-360\sqrt{3}}{2*180}=\frac{360-360\sqrt{3}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+360\sqrt{3}}{2*180}=\frac{360+360\sqrt{3}}{360}
$