2x(4x+2)-12=24

Solution for 2x(4x+2)-12=24 equation:

2x(4x+2)-12=24

We move all terms to the left:

2x(4x+2)-12-(24)=0

We add all the numbers together, and all the variables

2x(4x+2)-36=0

We multiply parentheses

8x^2+4x-36=0

a = 8; b = 4; c = -36;
Δ = b2-4ac
Δ = 42-4·8·(-36)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{73}}{2*8}=\frac{-4-4\sqrt{73}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{73}}{2*8}=\frac{-4+4\sqrt{73}}{16}
$