(360/x-180)x=1800

Solution for (360/x-180)x=1800 equation:

(360/x-180)x=1800

We move all terms to the left:

(360/x-180)x-(1800)=0


Domain of the equation: x-180)x!=0

x∈R


We multiply parentheses

360x^2-180x-1800=0

a = 360; b = -180; c = -1800;
Δ = b2-4ac
Δ = -1802-4·360·(-1800)
Δ = 2624400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2624400}=1620$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-1620}{2*360}=\frac{-1440}{720}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+1620}{2*360}=\frac{1800}{720}
=2+1/2
$