2x(6x+12)=288

Solution for 2x(6x+12)=288 equation:

2x(6x+12)=288

We move all terms to the left:

2x(6x+12)-(288)=0

We multiply parentheses

12x^2+24x-288=0

a = 12; b = 24; c = -288;
Δ = b2-4ac
Δ = 242-4·12·(-288)
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-120}{2*12}=\frac{-144}{24}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+120}{2*12}=\frac{96}{24}
=4
$