120x=(120-10x)(x+1)

Solution for 120x=(120-10x)(x+1) equation:

120x=(120-10x)(x+1)

We move all terms to the left:

120x-((120-10x)(x+1))=0

We add all the numbers together, and all the variables

120x-((-10x+120)(x+1))=0

We multiply parentheses ..

-((-10x^2-10x+120x+120))+120x=0


We calculate terms in parentheses: -((-10x^2-10x+120x+120)), so:

(-10x^2-10x+120x+120)

We get rid of parentheses

-10x^2-10x+120x+120

We add all the numbers together, and all the variables

-10x^2+110x+120

Back to the equation:

-(-10x^2+110x+120)


We get rid of parentheses

10x^2-110x+120x-120=0

We add all the numbers together, and all the variables

10x^2+10x-120=0

a = 10; b = 10; c = -120;
Δ = b2-4ac
Δ = 102-4·10·(-120)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-70}{2*10}=\frac{-80}{20}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+70}{2*10}=\frac{60}{20}
=3
$