x(360-x)=104

Solution for x(360-x)=104 equation:

x(360-x)=104

We move all terms to the left:

x(360-x)-(104)=0

We add all the numbers together, and all the variables

x(-1x+360)-104=0

We multiply parentheses

-1x^2+360x-104=0

a = -1; b = 360; c = -104;
Δ = b2-4ac
Δ = 3602-4·(-1)·(-104)
Δ = 129184
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:

$\sqrt{\Delta}=\sqrt{129184}=\sqrt{16*8074}=\sqrt{16}*\sqrt{8074}=4\sqrt{8074}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-4\sqrt{8074}}{2*-1}=\frac{-360-4\sqrt{8074}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+4\sqrt{8074}}{2*-1}=\frac{-360+4\sqrt{8074}}{-2}
$