(4x+12)(3x-2)=576

Solution for (4x+12)(3x-2)=576 equation:

(4x+12)(3x-2)=576

We move all terms to the left:

(4x+12)(3x-2)-(576)=0

We multiply parentheses ..

(+12x^2-8x+36x-24)-576=0

We get rid of parentheses

12x^2-8x+36x-24-576=0

We add all the numbers together, and all the variables

12x^2+28x-600=0

a = 12; b = 28; c = -600;
Δ = b2-4ac
Δ = 282-4·12·(-600)
Δ = 29584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29584}=172$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-172}{2*12}=\frac{-200}{24}
=-8+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+172}{2*12}=\frac{144}{24}
=6
$