1512=(120-2x)*x

Solution for 1512=(120-2x)*x equation:

1512=(120-2x)*x

We move all terms to the left:

1512-((120-2x)*x)=0

We add all the numbers together, and all the variables

-((-2x+120)*x)+1512=0


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

(-2x+120)*x

We multiply parentheses

-2x^2+120x

Back to the equation:

-(-2x^2+120x)


We get rid of parentheses

2x^2-120x+1512=0

a = 2; b = -120; c = +1512;
Δ = b2-4ac
Δ = -1202-4·2·1512
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-48}{2*2}=\frac{72}{4}
=18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+48}{2*2}=\frac{168}{4}
=42
$