(12+x)(120+3x)=2112

Solution for (12+x)(120+3x)=2112 equation:

(12+x)(120+3x)=2112

We move all terms to the left:

(12+x)(120+3x)-(2112)=0

We add all the numbers together, and all the variables

(x+12)(3x+120)-2112=0

We multiply parentheses ..

(+3x^2+120x+36x+1440)-2112=0

We get rid of parentheses

3x^2+120x+36x+1440-2112=0

We add all the numbers together, and all the variables

3x^2+156x-672=0

a = 3; b = 156; c = -672;
Δ = b2-4ac
Δ = 1562-4·3·(-672)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-180}{2*3}=\frac{-336}{6}
=-56
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+180}{2*3}=\frac{24}{6}
=4
$