(360/x+2)(x+6)=360

Solution for (360/x+2)(x+6)=360 equation:

(360/x+2)(x+6)=360

We move all terms to the left:

(360/x+2)(x+6)-(360)=0


Domain of the equation: x+2)(x+6)!=0

x∈R


We multiply parentheses ..

(+360x^2+2160x+2x+12)-360=0

We get rid of parentheses

360x^2+2160x+2x+12-360=0

We add all the numbers together, and all the variables

360x^2+2162x-348=0

a = 360; b = 2162; c = -348;
Δ = b2-4ac
Δ = 21622-4·360·(-348)
Δ = 5175364
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:

$\sqrt{\Delta}=\sqrt{5175364}=\sqrt{4*1293841}=\sqrt{4}*\sqrt{1293841}=2\sqrt{1293841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2162)-2\sqrt{1293841}}{2*360}=\frac{-2162-2\sqrt{1293841}}{720}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2162)+2\sqrt{1293841}}{2*360}=\frac{-2162+2\sqrt{1293841}}{720}
$