(360-2x)(x+30)=360x

Solution for (360-2x)(x+30)=360x equation:

(360-2x)(x+30)=360x

We move all terms to the left:

(360-2x)(x+30)-(360x)=0

We add all the numbers together, and all the variables

(-2x+360)(x+30)-360x=0

We add all the numbers together, and all the variables

-360x+(-2x+360)(x+30)=0

We multiply parentheses ..

(-2x^2-60x+360x+10800)-360x=0

We get rid of parentheses

-2x^2-60x+360x-360x+10800=0

We add all the numbers together, and all the variables

-2x^2-60x+10800=0

a = -2; b = -60; c = +10800;
Δ = b2-4ac
Δ = -602-4·(-2)·10800
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-300}{2*-2}=\frac{-240}{-4}
=+60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+300}{2*-2}=\frac{360}{-4}
=-90
$