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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We multiply parentheses

2x^2-8x+6x-24-12=0

We add all the numbers together, and all the variables

2x^2-2x-36=0

a = 2; b = -2; c = -36;
Δ = b2-4ac
Δ = -22-4·2·(-36)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{73}}{2*2}=\frac{2-2\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{73}}{2*2}=\frac{2+2\sqrt{73}}{4}
$