1500=x(120-2x)

Solution for 1500=x(120-2x) equation:

1500=x(120-2x)

We move all terms to the left:

1500-(x(120-2x))=0

We add all the numbers together, and all the variables

-(x(-2x+120))+1500=0


We calculate terms in parentheses: -(x(-2x+120)), so:

x(-2x+120)

We multiply parentheses

-2x^2+120x

Back to the equation:

-(-2x^2+120x)


We get rid of parentheses

2x^2-120x+1500=0

a = 2; b = -120; c = +1500;
Δ = b2-4ac
Δ = -1202-4·2·1500
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-20\sqrt{6}}{2*2}=\frac{120-20\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+20\sqrt{6}}{2*2}=\frac{120+20\sqrt{6}}{4}
$