1500=x(2x-120)

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

1500=x(2x-120)

We move all terms to the left:

1500-(x(2x-120))=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 = 26400
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:

$\sqrt{\Delta}=\sqrt{26400}=\sqrt{400*66}=\sqrt{400}*\sqrt{66}=20\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-20\sqrt{66}}{2*-2}=\frac{-120-20\sqrt{66}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+20\sqrt{66}}{2*-2}=\frac{-120+20\sqrt{66}}{-4}
$