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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-2x-22=0

a = 2; b = -2; c = -22;
Δ = b2-4ac
Δ = -22-4·2·(-22)
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6\sqrt{5}}{2*2}=\frac{2-6\sqrt{5}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6\sqrt{5}}{2*2}=\frac{2+6\sqrt{5}}{4}
$