180(x-2)+360/x=3780

Solution for 180(x-2)+360/x=3780 equation:

180(x-2)+360/x=3780

We move all terms to the left:

180(x-2)+360/x-(3780)=0


Domain of the equation: x!=0

x∈R


We multiply parentheses

180x+360/x-360-3780=0

We multiply all the terms by the denominator


180x*x-360*x-3780*x+360=0

We add all the numbers together, and all the variables

-4140x+180x*x+360=0

Wy multiply elements

180x^2-4140x+360=0

a = 180; b = -4140; c = +360;
Δ = b2-4ac
Δ = -41402-4·180·360
Δ = 16880400
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:

$\sqrt{\Delta}=\sqrt{16880400}=\sqrt{32400*521}=\sqrt{32400}*\sqrt{521}=180\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4140)-180\sqrt{521}}{2*180}=\frac{4140-180\sqrt{521}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4140)+180\sqrt{521}}{2*180}=\frac{4140+180\sqrt{521}}{360}
$