12x(3+x)=228

Solution for 12x(3+x)=228 equation:

12x(3+x)=228

We move all terms to the left:

12x(3+x)-(228)=0

We add all the numbers together, and all the variables

12x(x+3)-228=0

We multiply parentheses

12x^2+36x-228=0

a = 12; b = 36; c = -228;
Δ = b2-4ac
Δ = 362-4·12·(-228)
Δ = 12240
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:

$\sqrt{\Delta}=\sqrt{12240}=\sqrt{144*85}=\sqrt{144}*\sqrt{85}=12\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{85}}{2*12}=\frac{-36-12\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{85}}{2*12}=\frac{-36+12\sqrt{85}}{24}
$