x(240-x)=0

Solution for x(240-x)=0 equation:

x(240-x)=0

We add all the numbers together, and all the variables

x(-1x+240)=0

We multiply parentheses

-1x^2+240x=0

a = -1; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-1)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-1}=\frac{-480}{-2}
=+240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-1}=\frac{0}{-2}
=0
$