(12+x)(120+3x)=672

Solution for (12+x)(120+3x)=672 equation:

(12+x)(120+3x)=672

We move all terms to the left:

(12+x)(120+3x)-(672)=0

We add all the numbers together, and all the variables

(x+12)(3x+120)-672=0

We multiply parentheses ..

(+3x^2+120x+36x+1440)-672=0

We get rid of parentheses

3x^2+120x+36x+1440-672=0

We add all the numbers together, and all the variables

3x^2+156x+768=0

a = 3; b = 156; c = +768;
Δ = b2-4ac
Δ = 1562-4·3·768
Δ = 15120
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:

$\sqrt{\Delta}=\sqrt{15120}=\sqrt{144*105}=\sqrt{144}*\sqrt{105}=12\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(156)-12\sqrt{105}}{2*3}=\frac{-156-12\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(156)+12\sqrt{105}}{2*3}=\frac{-156+12\sqrt{105}}{6}
$