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

Solution for (360-2x)(x-6)-360=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+372x-2520=0

a = -2; b = 372; c = -2520;
Δ = b2-4ac
Δ = 3722-4·(-2)·(-2520)
Δ = 118224
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:

$\sqrt{\Delta}=\sqrt{118224}=\sqrt{144*821}=\sqrt{144}*\sqrt{821}=12\sqrt{821}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(372)-12\sqrt{821}}{2*-2}=\frac{-372-12\sqrt{821}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(372)+12\sqrt{821}}{2*-2}=\frac{-372+12\sqrt{821}}{-4}
$